Properties

Label 656.2.o.a.573.8
Level $656$
Weight $2$
Character 656.573
Analytic conductor $5.238$
Analytic rank $0$
Dimension $164$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [656,2,Mod(245,656)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(656, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("656.245");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 656.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: \(5.23818637260\)
Analytic rank: \(0\)
Dimension: \(164\)
Relative dimension: \(82\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 573.8
Character \(\chi\) \(=\) 656.573
Dual form 656.2.o.a.245.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37799 - 0.318038i) q^{2} +(1.64581 - 1.64581i) q^{3} +(1.79770 + 0.876504i) q^{4} +(1.05875 - 1.05875i) q^{5} +(-2.79134 + 1.74448i) q^{6} -0.937357 q^{7} +(-2.19845 - 1.77955i) q^{8} -2.41740i q^{9} +O(q^{10})\) \(q+(-1.37799 - 0.318038i) q^{2} +(1.64581 - 1.64581i) q^{3} +(1.79770 + 0.876504i) q^{4} +(1.05875 - 1.05875i) q^{5} +(-2.79134 + 1.74448i) q^{6} -0.937357 q^{7} +(-2.19845 - 1.77955i) q^{8} -2.41740i q^{9} +(-1.79567 + 1.12222i) q^{10} +(3.74605 + 3.74605i) q^{11} +(4.40124 - 1.51612i) q^{12} +(-0.659366 + 0.659366i) q^{13} +(1.29167 + 0.298115i) q^{14} -3.48501i q^{15} +(2.46348 + 3.15139i) q^{16} -5.56372i q^{17} +(-0.768823 + 3.33114i) q^{18} +(4.91609 - 4.91609i) q^{19} +(2.83132 - 0.975320i) q^{20} +(-1.54271 + 1.54271i) q^{21} +(-3.97063 - 6.35341i) q^{22} -7.92682i q^{23} +(-6.54705 + 0.689437i) q^{24} +2.75810i q^{25} +(1.11830 - 0.698895i) q^{26} +(0.958858 + 0.958858i) q^{27} +(-1.68509 - 0.821597i) q^{28} +(-0.225032 + 0.225032i) q^{29} +(-1.10836 + 4.80230i) q^{30} -6.94370 q^{31} +(-2.39239 - 5.12606i) q^{32} +12.3306 q^{33} +(-1.76947 + 7.66674i) q^{34} +(-0.992426 + 0.992426i) q^{35} +(2.11886 - 4.34576i) q^{36} +(6.02825 - 6.02825i) q^{37} +(-8.33781 + 5.21081i) q^{38} +2.17038i q^{39} +(-4.21171 + 0.443514i) q^{40} +(3.49691 + 5.36392i) q^{41} +(2.61648 - 1.63520i) q^{42} +(-6.60609 + 6.60609i) q^{43} +(3.45086 + 10.0177i) q^{44} +(-2.55942 - 2.55942i) q^{45} +(-2.52103 + 10.9231i) q^{46} -2.03944i q^{47} +(9.24102 + 1.13217i) q^{48} -6.12136 q^{49} +(0.877179 - 3.80063i) q^{50} +(-9.15684 - 9.15684i) q^{51} +(-1.76328 + 0.607408i) q^{52} +(8.26702 + 8.26702i) q^{53} +(-1.01634 - 1.62625i) q^{54} +7.93227 q^{55} +(2.06074 + 1.66807i) q^{56} -16.1819i q^{57} +(0.381659 - 0.238522i) q^{58} +(-1.96420 + 1.96420i) q^{59} +(3.05462 - 6.26501i) q^{60} +(-7.57484 - 7.57484i) q^{61} +(9.56834 + 2.20836i) q^{62} +2.26596i q^{63} +(1.66640 + 7.82452i) q^{64} +1.39621i q^{65} +(-16.9914 - 3.92160i) q^{66} +(-6.32499 + 6.32499i) q^{67} +(4.87663 - 10.0019i) q^{68} +(-13.0461 - 13.0461i) q^{69} +(1.68318 - 1.05192i) q^{70} -7.58361 q^{71} +(-4.30188 + 5.31453i) q^{72} -4.21740i q^{73} +(-10.2241 + 6.38964i) q^{74} +(4.53931 + 4.53931i) q^{75} +(13.1466 - 4.52870i) q^{76} +(-3.51139 - 3.51139i) q^{77} +(0.690264 - 2.99076i) q^{78} +4.13739i q^{79} +(5.94474 + 0.728325i) q^{80} +10.4084 q^{81} +(-3.11277 - 8.50357i) q^{82} +(-8.84563 - 8.84563i) q^{83} +(-4.12554 + 1.42115i) q^{84} +(-5.89059 - 5.89059i) q^{85} +(11.2041 - 7.00213i) q^{86} +0.740719i q^{87} +(-1.56924 - 14.9018i) q^{88} +17.2781 q^{89} +(2.71286 + 4.34084i) q^{90} +(0.618061 - 0.618061i) q^{91} +(6.94789 - 14.2501i) q^{92} +(-11.4280 + 11.4280i) q^{93} +(-0.648617 + 2.81032i) q^{94} -10.4098i q^{95} +(-12.3740 - 4.49911i) q^{96} +3.29849i q^{97} +(8.43517 + 1.94682i) q^{98} +(9.05570 - 9.05570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 164 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 164 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 16 q^{8} - 16 q^{10} - 4 q^{16} + 4 q^{18} - 4 q^{20} - 16 q^{21} - 32 q^{31} + 16 q^{32} - 8 q^{33} + 40 q^{36} - 4 q^{37} - 44 q^{40} + 52 q^{42} - 36 q^{43} + 28 q^{45} - 16 q^{46} + 132 q^{49} + 16 q^{50} + 8 q^{51} + 20 q^{59} - 4 q^{61} - 48 q^{62} + 68 q^{64} + 76 q^{66} + 20 q^{72} - 56 q^{74} - 32 q^{77} - 8 q^{78} - 100 q^{80} - 140 q^{81} + 44 q^{82} - 4 q^{83} - 40 q^{84} - 12 q^{86} - 8 q^{90} - 80 q^{91} + 112 q^{92} - 136 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/656\mathbb{Z}\right)^\times\).

\(n\) \(129\) \(165\) \(575\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37799 0.318038i −0.974385 0.224887i
\(3\) 1.64581 1.64581i 0.950210 0.950210i −0.0486078 0.998818i \(-0.515478\pi\)
0.998818 + 0.0486078i \(0.0154785\pi\)
\(4\) 1.79770 + 0.876504i 0.898852 + 0.438252i
\(5\) 1.05875 1.05875i 0.473487 0.473487i −0.429554 0.903041i \(-0.641329\pi\)
0.903041 + 0.429554i \(0.141329\pi\)
\(6\) −2.79134 + 1.74448i −1.13956 + 0.712181i
\(7\) −0.937357 −0.354288 −0.177144 0.984185i \(-0.556686\pi\)
−0.177144 + 0.984185i \(0.556686\pi\)
\(8\) −2.19845 1.77955i −0.777271 0.629166i
\(9\) 2.41740i 0.805799i
\(10\) −1.79567 + 1.12222i −0.567840 + 0.354878i
\(11\) 3.74605 + 3.74605i 1.12948 + 1.12948i 0.990262 + 0.139216i \(0.0444582\pi\)
0.139216 + 0.990262i \(0.455542\pi\)
\(12\) 4.40124 1.51612i 1.27053 0.437667i
\(13\) −0.659366 + 0.659366i −0.182875 + 0.182875i −0.792607 0.609732i \(-0.791277\pi\)
0.609732 + 0.792607i \(0.291277\pi\)
\(14\) 1.29167 + 0.298115i 0.345213 + 0.0796745i
\(15\) 3.48501i 0.899825i
\(16\) 2.46348 + 3.15139i 0.615870 + 0.787848i
\(17\) 5.56372i 1.34940i −0.738092 0.674700i \(-0.764273\pi\)
0.738092 0.674700i \(-0.235727\pi\)
\(18\) −0.768823 + 3.33114i −0.181213 + 0.785158i
\(19\) 4.91609 4.91609i 1.12783 1.12783i 0.137298 0.990530i \(-0.456158\pi\)
0.990530 0.137298i \(-0.0438418\pi\)
\(20\) 2.83132 0.975320i 0.633102 0.218088i
\(21\) −1.54271 + 1.54271i −0.336648 + 0.336648i
\(22\) −3.97063 6.35341i −0.846542 1.35455i
\(23\) 7.92682i 1.65286i −0.563042 0.826428i \(-0.690369\pi\)
0.563042 0.826428i \(-0.309631\pi\)
\(24\) −6.54705 + 0.689437i −1.33641 + 0.140731i
\(25\) 2.75810i 0.551620i
\(26\) 1.11830 0.698895i 0.219317 0.137065i
\(27\) 0.958858 + 0.958858i 0.184532 + 0.184532i
\(28\) −1.68509 0.821597i −0.318452 0.155267i
\(29\) −0.225032 + 0.225032i −0.0417873 + 0.0417873i −0.727692 0.685904i \(-0.759407\pi\)
0.685904 + 0.727692i \(0.259407\pi\)
\(30\) −1.10836 + 4.80230i −0.202358 + 0.876776i
\(31\) −6.94370 −1.24713 −0.623563 0.781773i \(-0.714316\pi\)
−0.623563 + 0.781773i \(0.714316\pi\)
\(32\) −2.39239 5.12606i −0.422918 0.906168i
\(33\) 12.3306 2.14648
\(34\) −1.76947 + 7.66674i −0.303462 + 1.31484i
\(35\) −0.992426 + 0.992426i −0.167751 + 0.167751i
\(36\) 2.11886 4.34576i 0.353143 0.724294i
\(37\) 6.02825 6.02825i 0.991037 0.991037i −0.00892271 0.999960i \(-0.502840\pi\)
0.999960 + 0.00892271i \(0.00284022\pi\)
\(38\) −8.33781 + 5.21081i −1.35257 + 0.845305i
\(39\) 2.17038i 0.347540i
\(40\) −4.21171 + 0.443514i −0.665930 + 0.0701258i
\(41\) 3.49691 + 5.36392i 0.546125 + 0.837704i
\(42\) 2.61648 1.63520i 0.403732 0.252317i
\(43\) −6.60609 + 6.60609i −1.00742 + 1.00742i −0.00744625 + 0.999972i \(0.502370\pi\)
−0.999972 + 0.00744625i \(0.997630\pi\)
\(44\) 3.45086 + 10.0177i 0.520237 + 1.51023i
\(45\) −2.55942 2.55942i −0.381535 0.381535i
\(46\) −2.52103 + 10.9231i −0.371705 + 1.61052i
\(47\) 2.03944i 0.297482i −0.988876 0.148741i \(-0.952478\pi\)
0.988876 0.148741i \(-0.0475221\pi\)
\(48\) 9.24102 + 1.13217i 1.33383 + 0.163415i
\(49\) −6.12136 −0.874480
\(50\) 0.877179 3.80063i 0.124052 0.537490i
\(51\) −9.15684 9.15684i −1.28221 1.28221i
\(52\) −1.76328 + 0.607408i −0.244523 + 0.0842323i
\(53\) 8.26702 + 8.26702i 1.13556 + 1.13556i 0.989236 + 0.146326i \(0.0467448\pi\)
0.146326 + 0.989236i \(0.453255\pi\)
\(54\) −1.01634 1.62625i −0.138307 0.221304i
\(55\) 7.93227 1.06959
\(56\) 2.06074 + 1.66807i 0.275377 + 0.222906i
\(57\) 16.1819i 2.14335i
\(58\) 0.381659 0.238522i 0.0501143 0.0313195i
\(59\) −1.96420 + 1.96420i −0.255717 + 0.255717i −0.823310 0.567592i \(-0.807875\pi\)
0.567592 + 0.823310i \(0.307875\pi\)
\(60\) 3.05462 6.26501i 0.394350 0.808809i
\(61\) −7.57484 7.57484i −0.969859 0.969859i 0.0297000 0.999559i \(-0.490545\pi\)
−0.999559 + 0.0297000i \(0.990545\pi\)
\(62\) 9.56834 + 2.20836i 1.21518 + 0.280462i
\(63\) 2.26596i 0.285484i
\(64\) 1.66640 + 7.82452i 0.208300 + 0.978065i
\(65\) 1.39621i 0.173178i
\(66\) −16.9914 3.92160i −2.09150 0.482715i
\(67\) −6.32499 + 6.32499i −0.772721 + 0.772721i −0.978581 0.205861i \(-0.934001\pi\)
0.205861 + 0.978581i \(0.434001\pi\)
\(68\) 4.87663 10.0019i 0.591378 1.21291i
\(69\) −13.0461 13.0461i −1.57056 1.57056i
\(70\) 1.68318 1.05192i 0.201179 0.125729i
\(71\) −7.58361 −0.900009 −0.450005 0.893026i \(-0.648578\pi\)
−0.450005 + 0.893026i \(0.648578\pi\)
\(72\) −4.30188 + 5.31453i −0.506981 + 0.626324i
\(73\) 4.21740i 0.493610i −0.969065 0.246805i \(-0.920619\pi\)
0.969065 0.246805i \(-0.0793807\pi\)
\(74\) −10.2241 + 6.38964i −1.18852 + 0.742781i
\(75\) 4.53931 + 4.53931i 0.524155 + 0.524155i
\(76\) 13.1466 4.52870i 1.50802 0.519477i
\(77\) −3.51139 3.51139i −0.400160 0.400160i
\(78\) 0.690264 2.99076i 0.0781570 0.338637i
\(79\) 4.13739i 0.465493i 0.972537 + 0.232746i \(0.0747712\pi\)
−0.972537 + 0.232746i \(0.925229\pi\)
\(80\) 5.94474 + 0.728325i 0.664642 + 0.0814292i
\(81\) 10.4084 1.15649
\(82\) −3.11277 8.50357i −0.343748 0.939062i
\(83\) −8.84563 8.84563i −0.970934 0.970934i 0.0286550 0.999589i \(-0.490878\pi\)
−0.999589 + 0.0286550i \(0.990878\pi\)
\(84\) −4.12554 + 1.42115i −0.450133 + 0.155060i
\(85\) −5.89059 5.89059i −0.638924 0.638924i
\(86\) 11.2041 7.00213i 1.20817 0.755059i
\(87\) 0.740719i 0.0794135i
\(88\) −1.56924 14.9018i −0.167281 1.58854i
\(89\) 17.2781 1.83147 0.915736 0.401781i \(-0.131609\pi\)
0.915736 + 0.401781i \(0.131609\pi\)
\(90\) 2.71286 + 4.34084i 0.285960 + 0.457564i
\(91\) 0.618061 0.618061i 0.0647904 0.0647904i
\(92\) 6.94789 14.2501i 0.724368 1.48567i
\(93\) −11.4280 + 11.4280i −1.18503 + 1.18503i
\(94\) −0.648617 + 2.81032i −0.0668998 + 0.289862i
\(95\) 10.4098i 1.06802i
\(96\) −12.3740 4.49911i −1.26291 0.459189i
\(97\) 3.29849i 0.334911i 0.985880 + 0.167455i \(0.0535550\pi\)
−0.985880 + 0.167455i \(0.946445\pi\)
\(98\) 8.43517 + 1.94682i 0.852080 + 0.196659i
\(99\) 9.05570 9.05570i 0.910132 0.910132i
\(100\) −2.41749 + 4.95825i −0.241749 + 0.495825i
\(101\) 5.42968 + 5.42968i 0.540274 + 0.540274i 0.923609 0.383336i \(-0.125225\pi\)
−0.383336 + 0.923609i \(0.625225\pi\)
\(102\) 9.70580 + 15.5302i 0.961018 + 1.53772i
\(103\) 14.8634i 1.46453i 0.681020 + 0.732265i \(0.261537\pi\)
−0.681020 + 0.732265i \(0.738463\pi\)
\(104\) 2.62296 0.276211i 0.257202 0.0270847i
\(105\) 3.26669i 0.318797i
\(106\) −8.76263 14.0211i −0.851102 1.36185i
\(107\) 6.02159 6.02159i 0.582129 0.582129i −0.353359 0.935488i \(-0.614960\pi\)
0.935488 + 0.353359i \(0.114960\pi\)
\(108\) 0.883299 + 2.56419i 0.0849955 + 0.246739i
\(109\) −0.319278 + 0.319278i −0.0305813 + 0.0305813i −0.722232 0.691651i \(-0.756884\pi\)
0.691651 + 0.722232i \(0.256884\pi\)
\(110\) −10.9306 2.52276i −1.04219 0.240536i
\(111\) 19.8427i 1.88339i
\(112\) −2.30916 2.95398i −0.218195 0.279125i
\(113\) 10.1953 0.959089 0.479544 0.877518i \(-0.340802\pi\)
0.479544 + 0.877518i \(0.340802\pi\)
\(114\) −5.14646 + 22.2985i −0.482010 + 2.08844i
\(115\) −8.39252 8.39252i −0.782607 0.782607i
\(116\) −0.601781 + 0.207299i −0.0558740 + 0.0192472i
\(117\) 1.59395 + 1.59395i 0.147361 + 0.147361i
\(118\) 3.33134 2.08196i 0.306674 0.191660i
\(119\) 5.21519i 0.478076i
\(120\) −6.20174 + 7.66163i −0.566139 + 0.699408i
\(121\) 17.0659i 1.55144i
\(122\) 8.02896 + 12.8471i 0.726908 + 1.16312i
\(123\) 14.5833 + 3.07276i 1.31493 + 0.277061i
\(124\) −12.4827 6.08619i −1.12098 0.546556i
\(125\) 8.21388 + 8.21388i 0.734672 + 0.734672i
\(126\) 0.720661 3.12247i 0.0642016 0.278172i
\(127\) −1.86845 −0.165798 −0.0828992 0.996558i \(-0.526418\pi\)
−0.0828992 + 0.996558i \(0.526418\pi\)
\(128\) 0.192210 11.3121i 0.0169891 0.999856i
\(129\) 21.7448i 1.91452i
\(130\) 0.444046 1.92396i 0.0389454 0.168742i
\(131\) 6.76621 + 6.76621i 0.591167 + 0.591167i 0.937947 0.346780i \(-0.112725\pi\)
−0.346780 + 0.937947i \(0.612725\pi\)
\(132\) 22.1668 + 10.8078i 1.92937 + 0.940701i
\(133\) −4.60813 + 4.60813i −0.399575 + 0.399575i
\(134\) 10.7273 6.70418i 0.926702 0.579153i
\(135\) 2.03038 0.174747
\(136\) −9.90092 + 12.2316i −0.848997 + 1.04885i
\(137\) 2.18124 0.186356 0.0931781 0.995649i \(-0.470297\pi\)
0.0931781 + 0.995649i \(0.470297\pi\)
\(138\) 13.8282 + 22.1265i 1.17713 + 1.88353i
\(139\) −9.50390 + 9.50390i −0.806110 + 0.806110i −0.984043 0.177933i \(-0.943059\pi\)
0.177933 + 0.984043i \(0.443059\pi\)
\(140\) −2.65396 + 0.914223i −0.224300 + 0.0772659i
\(141\) −3.35653 3.35653i −0.282671 0.282671i
\(142\) 10.4501 + 2.41187i 0.876956 + 0.202400i
\(143\) −4.94004 −0.413107
\(144\) 7.61816 5.95521i 0.634847 0.496267i
\(145\) 0.476504i 0.0395715i
\(146\) −1.34129 + 5.81153i −0.111006 + 0.480966i
\(147\) −10.0746 + 10.0746i −0.830940 + 0.830940i
\(148\) 16.1208 5.55322i 1.32512 0.456472i
\(149\) 3.26161 + 3.26161i 0.267201 + 0.267201i 0.827971 0.560770i \(-0.189495\pi\)
−0.560770 + 0.827971i \(0.689495\pi\)
\(150\) −4.81145 7.69879i −0.392853 0.628604i
\(151\) −22.2846 −1.81350 −0.906748 0.421672i \(-0.861443\pi\)
−0.906748 + 0.421672i \(0.861443\pi\)
\(152\) −19.5562 + 2.05937i −1.58622 + 0.167037i
\(153\) −13.4497 −1.08735
\(154\) 3.72190 + 5.95541i 0.299919 + 0.479901i
\(155\) −7.35164 + 7.35164i −0.590498 + 0.590498i
\(156\) −1.90235 + 3.90171i −0.152310 + 0.312387i
\(157\) 4.67424 4.67424i 0.373045 0.373045i −0.495540 0.868585i \(-0.665030\pi\)
0.868585 + 0.495540i \(0.165030\pi\)
\(158\) 1.31585 5.70128i 0.104683 0.453569i
\(159\) 27.2119 2.15805
\(160\) −7.96015 2.89428i −0.629305 0.228813i
\(161\) 7.43026i 0.585587i
\(162\) −14.3426 3.31026i −1.12686 0.260078i
\(163\) 1.78040 + 1.78040i 0.139451 + 0.139451i 0.773386 0.633935i \(-0.218561\pi\)
−0.633935 + 0.773386i \(0.718561\pi\)
\(164\) 1.58490 + 12.7078i 0.123760 + 0.992312i
\(165\) 13.0550 13.0550i 1.01633 1.01633i
\(166\) 9.37594 + 15.0024i 0.727714 + 1.16441i
\(167\) −14.7022 −1.13769 −0.568846 0.822444i \(-0.692610\pi\)
−0.568846 + 0.822444i \(0.692610\pi\)
\(168\) 6.13692 0.646249i 0.473474 0.0498592i
\(169\) 12.1305i 0.933113i
\(170\) 6.24373 + 9.99059i 0.478873 + 0.766243i
\(171\) −11.8841 11.8841i −0.908802 0.908802i
\(172\) −17.6660 + 6.08552i −1.34702 + 0.464017i
\(173\) −3.32221 3.32221i −0.252583 0.252583i 0.569446 0.822029i \(-0.307158\pi\)
−0.822029 + 0.569446i \(0.807158\pi\)
\(174\) 0.235577 1.02070i 0.0178590 0.0773793i
\(175\) 2.58532i 0.195432i
\(176\) −2.57695 + 21.0336i −0.194245 + 1.58547i
\(177\) 6.46541i 0.485970i
\(178\) −23.8090 5.49508i −1.78456 0.411873i
\(179\) 10.7296 10.7296i 0.801968 0.801968i −0.181435 0.983403i \(-0.558074\pi\)
0.983403 + 0.181435i \(0.0580741\pi\)
\(180\) −2.35773 6.84441i −0.175735 0.510152i
\(181\) −3.45819 3.45819i −0.257045 0.257045i 0.566806 0.823851i \(-0.308179\pi\)
−0.823851 + 0.566806i \(0.808179\pi\)
\(182\) −1.04825 + 0.655114i −0.0777013 + 0.0485603i
\(183\) −24.9335 −1.84314
\(184\) −14.1062 + 17.4268i −1.03992 + 1.28472i
\(185\) 12.7648i 0.938487i
\(186\) 19.3822 12.1132i 1.42117 0.888179i
\(187\) 20.8420 20.8420i 1.52412 1.52412i
\(188\) 1.78757 3.66630i 0.130372 0.267393i
\(189\) −0.898792 0.898792i −0.0653775 0.0653775i
\(190\) −3.31071 + 14.3446i −0.240184 + 1.04067i
\(191\) 15.7205i 1.13750i 0.822512 + 0.568748i \(0.192572\pi\)
−0.822512 + 0.568748i \(0.807428\pi\)
\(192\) 15.6203 + 10.1351i 1.12730 + 0.731438i
\(193\) 0.977304i 0.0703479i 0.999381 + 0.0351739i \(0.0111985\pi\)
−0.999381 + 0.0351739i \(0.988801\pi\)
\(194\) 1.04904 4.54528i 0.0753169 0.326332i
\(195\) 2.29789 + 2.29789i 0.164556 + 0.164556i
\(196\) −11.0044 5.36540i −0.786028 0.383243i
\(197\) −17.4268 + 17.4268i −1.24161 + 1.24161i −0.282271 + 0.959335i \(0.591088\pi\)
−0.959335 + 0.282271i \(0.908912\pi\)
\(198\) −15.3587 + 9.59859i −1.09149 + 0.682142i
\(199\) 23.6963 1.67979 0.839894 0.542751i \(-0.182617\pi\)
0.839894 + 0.542751i \(0.182617\pi\)
\(200\) 4.90818 6.06355i 0.347060 0.428758i
\(201\) 20.8195i 1.46849i
\(202\) −5.75520 9.20888i −0.404934 0.647935i
\(203\) 0.210935 0.210935i 0.0148047 0.0148047i
\(204\) −8.43528 24.4873i −0.590588 1.71445i
\(205\) 9.38140 + 1.97670i 0.655225 + 0.138059i
\(206\) 4.72711 20.4815i 0.329353 1.42702i
\(207\) −19.1623 −1.33187
\(208\) −3.70225 0.453585i −0.256705 0.0314504i
\(209\) 36.8319 2.54771
\(210\) 1.03893 4.50147i 0.0716931 0.310631i
\(211\) −1.05855 + 1.05855i −0.0728738 + 0.0728738i −0.742604 0.669730i \(-0.766410\pi\)
0.669730 + 0.742604i \(0.266410\pi\)
\(212\) 7.61558 + 22.1077i 0.523040 + 1.51837i
\(213\) −12.4812 + 12.4812i −0.855198 + 0.855198i
\(214\) −10.2128 + 6.38259i −0.698131 + 0.436305i
\(215\) 13.9884i 0.954000i
\(216\) −0.401669 3.81434i −0.0273301 0.259533i
\(217\) 6.50873 0.441841
\(218\) 0.541504 0.338419i 0.0366753 0.0229206i
\(219\) −6.94105 6.94105i −0.469033 0.469033i
\(220\) 14.2599 + 6.95267i 0.961400 + 0.468749i
\(221\) 3.66853 + 3.66853i 0.246772 + 0.246772i
\(222\) −6.31073 + 27.3430i −0.423549 + 1.83514i
\(223\) −7.80529 −0.522681 −0.261340 0.965247i \(-0.584165\pi\)
−0.261340 + 0.965247i \(0.584165\pi\)
\(224\) 2.24252 + 4.80495i 0.149835 + 0.321044i
\(225\) 6.66741 0.444494
\(226\) −14.0489 3.24247i −0.934522 0.215686i
\(227\) 7.02985 7.02985i 0.466587 0.466587i −0.434220 0.900807i \(-0.642976\pi\)
0.900807 + 0.434220i \(0.142976\pi\)
\(228\) 14.1835 29.0903i 0.939326 1.92655i
\(229\) 12.2934 + 12.2934i 0.812373 + 0.812373i 0.984989 0.172616i \(-0.0552220\pi\)
−0.172616 + 0.984989i \(0.555222\pi\)
\(230\) 8.89566 + 14.2339i 0.586562 + 0.938558i
\(231\) −11.5582 −0.760472
\(232\) 0.895177 0.0942666i 0.0587712 0.00618890i
\(233\) 2.38502 0.156248 0.0781239 0.996944i \(-0.475107\pi\)
0.0781239 + 0.996944i \(0.475107\pi\)
\(234\) −1.68951 2.70338i −0.110446 0.176725i
\(235\) −2.15925 2.15925i −0.140854 0.140854i
\(236\) −5.25269 + 1.80942i −0.341921 + 0.117783i
\(237\) 6.80937 + 6.80937i 0.442316 + 0.442316i
\(238\) 1.65863 7.18648i 0.107513 0.465830i
\(239\) 9.45338i 0.611488i −0.952114 0.305744i \(-0.901095\pi\)
0.952114 0.305744i \(-0.0989052\pi\)
\(240\) 10.9826 8.58524i 0.708925 0.554175i
\(241\) 14.8486 0.956484 0.478242 0.878228i \(-0.341274\pi\)
0.478242 + 0.878228i \(0.341274\pi\)
\(242\) 5.42758 23.5165i 0.348898 1.51170i
\(243\) 14.2537 14.2537i 0.914374 0.914374i
\(244\) −6.97794 20.2567i −0.446717 1.29680i
\(245\) −6.48099 + 6.48099i −0.414055 + 0.414055i
\(246\) −19.1183 8.87225i −1.21894 0.565674i
\(247\) 6.48300i 0.412503i
\(248\) 15.2654 + 12.3567i 0.969355 + 0.784649i
\(249\) −29.1165 −1.84518
\(250\) −8.70631 13.9310i −0.550636 0.881071i
\(251\) −1.35201 + 1.35201i −0.0853383 + 0.0853383i −0.748487 0.663149i \(-0.769220\pi\)
0.663149 + 0.748487i \(0.269220\pi\)
\(252\) −1.98613 + 4.07353i −0.125114 + 0.256608i
\(253\) 29.6943 29.6943i 1.86687 1.86687i
\(254\) 2.57471 + 0.594238i 0.161551 + 0.0372858i
\(255\) −19.3896 −1.21422
\(256\) −3.86253 + 15.5268i −0.241408 + 0.970424i
\(257\) 17.5287i 1.09341i 0.837325 + 0.546706i \(0.184118\pi\)
−0.837325 + 0.546706i \(0.815882\pi\)
\(258\) 6.91565 29.9640i 0.430549 1.86548i
\(259\) −5.65062 + 5.65062i −0.351112 + 0.351112i
\(260\) −1.22378 + 2.50997i −0.0758957 + 0.155662i
\(261\) 0.543990 + 0.543990i 0.0336722 + 0.0336722i
\(262\) −7.17185 11.4757i −0.443079 0.708970i
\(263\) 9.33597 0.575681 0.287840 0.957678i \(-0.407063\pi\)
0.287840 + 0.957678i \(0.407063\pi\)
\(264\) −27.1083 21.9429i −1.66840 1.35049i
\(265\) 17.5054 1.07535
\(266\) 7.81551 4.88439i 0.479200 0.299481i
\(267\) 28.4365 28.4365i 1.74028 1.74028i
\(268\) −16.9143 + 5.82658i −1.03321 + 0.355915i
\(269\) −1.79282 1.79282i −0.109310 0.109310i 0.650336 0.759646i \(-0.274628\pi\)
−0.759646 + 0.650336i \(0.774628\pi\)
\(270\) −2.79784 0.645737i −0.170271 0.0392983i
\(271\) −25.0064 −1.51903 −0.759515 0.650490i \(-0.774563\pi\)
−0.759515 + 0.650490i \(0.774563\pi\)
\(272\) 17.5335 13.7061i 1.06312 0.831056i
\(273\) 2.03443i 0.123129i
\(274\) −3.00573 0.693717i −0.181583 0.0419090i
\(275\) −10.3320 + 10.3320i −0.623042 + 0.623042i
\(276\) −12.0180 34.8879i −0.723400 2.10000i
\(277\) −0.245403 + 0.245403i −0.0147448 + 0.0147448i −0.714441 0.699696i \(-0.753319\pi\)
0.699696 + 0.714441i \(0.253319\pi\)
\(278\) 16.1189 10.0737i 0.966745 0.604178i
\(279\) 16.7857i 1.00493i
\(280\) 3.94788 0.415731i 0.235931 0.0248447i
\(281\) −18.0981 −1.07964 −0.539821 0.841780i \(-0.681508\pi\)
−0.539821 + 0.841780i \(0.681508\pi\)
\(282\) 3.55776 + 5.69276i 0.211861 + 0.338999i
\(283\) −5.83493 + 5.83493i −0.346850 + 0.346850i −0.858935 0.512085i \(-0.828873\pi\)
0.512085 + 0.858935i \(0.328873\pi\)
\(284\) −13.6331 6.64707i −0.808975 0.394431i
\(285\) −17.1326 17.1326i −1.01485 1.01485i
\(286\) 6.80732 + 1.57112i 0.402525 + 0.0929022i
\(287\) −3.27785 5.02791i −0.193485 0.296788i
\(288\) −12.3917 + 5.78334i −0.730189 + 0.340787i
\(289\) −13.9550 −0.820883
\(290\) 0.151546 0.656617i 0.00889910 0.0385579i
\(291\) 5.42869 + 5.42869i 0.318235 + 0.318235i
\(292\) 3.69657 7.58164i 0.216325 0.443682i
\(293\) −12.9628 12.9628i −0.757297 0.757297i 0.218532 0.975830i \(-0.429873\pi\)
−0.975830 + 0.218532i \(0.929873\pi\)
\(294\) 17.0868 10.6786i 0.996523 0.622788i
\(295\) 4.15920i 0.242158i
\(296\) −23.9804 + 2.52526i −1.39383 + 0.146777i
\(297\) 7.18387i 0.416850i
\(298\) −3.45714 5.53177i −0.200267 0.320447i
\(299\) 5.22668 + 5.22668i 0.302266 + 0.302266i
\(300\) 4.18161 + 12.1391i 0.241426 + 0.700849i
\(301\) 6.19226 6.19226i 0.356916 0.356916i
\(302\) 30.7079 + 7.08735i 1.76704 + 0.407831i
\(303\) 17.8725 1.02675
\(304\) 27.6032 + 3.38183i 1.58315 + 0.193961i
\(305\) −16.0397 −0.918432
\(306\) 18.5336 + 4.27752i 1.05949 + 0.244529i
\(307\) 15.1662 + 15.1662i 0.865581 + 0.865581i 0.991980 0.126398i \(-0.0403417\pi\)
−0.126398 + 0.991980i \(0.540342\pi\)
\(308\) −3.23469 9.39019i −0.184314 0.535056i
\(309\) 24.4623 + 24.4623i 1.39161 + 1.39161i
\(310\) 12.4686 7.79238i 0.708168 0.442578i
\(311\) −10.1110 −0.573341 −0.286671 0.958029i \(-0.592549\pi\)
−0.286671 + 0.958029i \(0.592549\pi\)
\(312\) 3.86231 4.77149i 0.218660 0.270132i
\(313\) −8.01296 −0.452919 −0.226460 0.974021i \(-0.572715\pi\)
−0.226460 + 0.974021i \(0.572715\pi\)
\(314\) −7.92764 + 4.95447i −0.447383 + 0.279597i
\(315\) 2.39909 + 2.39909i 0.135173 + 0.135173i
\(316\) −3.62644 + 7.43781i −0.204003 + 0.418409i
\(317\) −5.50093 + 5.50093i −0.308963 + 0.308963i −0.844507 0.535544i \(-0.820107\pi\)
0.535544 + 0.844507i \(0.320107\pi\)
\(318\) −37.4977 8.65441i −2.10277 0.485315i
\(319\) −1.68596 −0.0943957
\(320\) 10.0485 + 6.51991i 0.561729 + 0.364474i
\(321\) 19.8208i 1.10629i
\(322\) 2.36310 10.2388i 0.131691 0.570587i
\(323\) −27.3517 27.3517i −1.52189 1.52189i
\(324\) 18.7112 + 9.12299i 1.03951 + 0.506833i
\(325\) −1.81860 1.81860i −0.100878 0.100878i
\(326\) −1.88713 3.01960i −0.104519 0.167240i
\(327\) 1.05094i 0.0581173i
\(328\) 1.85758 18.0153i 0.102568 0.994726i
\(329\) 1.91168i 0.105394i
\(330\) −22.1417 + 13.8377i −1.21886 + 0.761739i
\(331\) −19.4013 19.4013i −1.06639 1.06639i −0.997633 0.0687577i \(-0.978096\pi\)
−0.0687577 0.997633i \(-0.521904\pi\)
\(332\) −8.14860 23.6551i −0.447212 1.29824i
\(333\) −14.5727 14.5727i −0.798577 0.798577i
\(334\) 20.2595 + 4.67586i 1.10855 + 0.255852i
\(335\) 13.3932i 0.731747i
\(336\) −8.66214 1.06125i −0.472558 0.0578959i
\(337\) 6.67510 0.363616 0.181808 0.983334i \(-0.441805\pi\)
0.181808 + 0.983334i \(0.441805\pi\)
\(338\) 3.85795 16.7157i 0.209845 0.909212i
\(339\) 16.7795 16.7795i 0.911336 0.911336i
\(340\) −5.42641 15.7527i −0.294288 0.854308i
\(341\) −26.0115 26.0115i −1.40860 1.40860i
\(342\) 12.5966 + 20.1558i 0.681146 + 1.08990i
\(343\) 12.2994 0.664105
\(344\) 26.2790 2.76731i 1.41687 0.149204i
\(345\) −27.6250 −1.48728
\(346\) 3.52138 + 5.63456i 0.189311 + 0.302916i
\(347\) −5.77407 5.77407i −0.309968 0.309968i 0.534929 0.844897i \(-0.320338\pi\)
−0.844897 + 0.534929i \(0.820338\pi\)
\(348\) −0.649244 + 1.33159i −0.0348031 + 0.0713810i
\(349\) 10.0447 + 10.0447i 0.537683 + 0.537683i 0.922848 0.385165i \(-0.125855\pi\)
−0.385165 + 0.922848i \(0.625855\pi\)
\(350\) −0.822230 + 3.56255i −0.0439500 + 0.190426i
\(351\) −1.26448 −0.0674927
\(352\) 10.2405 28.1645i 0.545820 1.50117i
\(353\) −9.60947 −0.511460 −0.255730 0.966748i \(-0.582316\pi\)
−0.255730 + 0.966748i \(0.582316\pi\)
\(354\) 2.05625 8.90927i 0.109288 0.473522i
\(355\) −8.02915 + 8.02915i −0.426143 + 0.426143i
\(356\) 31.0609 + 15.1443i 1.64622 + 0.802646i
\(357\) 8.58323 + 8.58323i 0.454273 + 0.454273i
\(358\) −18.1977 + 11.3729i −0.961778 + 0.601074i
\(359\) 24.2866i 1.28180i 0.767625 + 0.640899i \(0.221438\pi\)
−0.767625 + 0.640899i \(0.778562\pi\)
\(360\) 1.07215 + 10.1814i 0.0565072 + 0.536605i
\(361\) 29.3358i 1.54399i
\(362\) 3.66551 + 5.86517i 0.192655 + 0.308267i
\(363\) 28.0872 + 28.0872i 1.47419 + 1.47419i
\(364\) 1.65282 0.569358i 0.0866315 0.0298425i
\(365\) −4.46517 4.46517i −0.233718 0.233718i
\(366\) 34.3581 + 7.92980i 1.79593 + 0.414497i
\(367\) 23.9412 1.24972 0.624860 0.780737i \(-0.285156\pi\)
0.624860 + 0.780737i \(0.285156\pi\)
\(368\) 24.9805 19.5276i 1.30220 1.01795i
\(369\) 12.9667 8.45340i 0.675020 0.440067i
\(370\) −4.05969 + 17.5898i −0.211053 + 0.914448i
\(371\) −7.74915 7.74915i −0.402316 0.402316i
\(372\) −30.5609 + 10.5275i −1.58451 + 0.545826i
\(373\) 13.1053 13.1053i 0.678566 0.678566i −0.281110 0.959676i \(-0.590702\pi\)
0.959676 + 0.281110i \(0.0907024\pi\)
\(374\) −35.3486 + 22.0915i −1.82783 + 1.14232i
\(375\) 27.0370 1.39619
\(376\) −3.62928 + 4.48361i −0.187166 + 0.231224i
\(377\) 0.296756i 0.0152837i
\(378\) 0.952675 + 1.52437i 0.0490003 + 0.0784054i
\(379\) 11.3137 11.3137i 0.581148 0.581148i −0.354070 0.935219i \(-0.615203\pi\)
0.935219 + 0.354070i \(0.115203\pi\)
\(380\) 9.12425 18.7138i 0.468064 0.959996i
\(381\) −3.07512 + 3.07512i −0.157543 + 0.157543i
\(382\) 4.99971 21.6627i 0.255808 1.10836i
\(383\) 3.91158i 0.199873i 0.994994 + 0.0999363i \(0.0318639\pi\)
−0.994994 + 0.0999363i \(0.968136\pi\)
\(384\) −18.3012 18.9339i −0.933930 0.966216i
\(385\) −7.43537 −0.378941
\(386\) 0.310819 1.34671i 0.0158203 0.0685459i
\(387\) 15.9695 + 15.9695i 0.811776 + 0.811776i
\(388\) −2.89114 + 5.92970i −0.146775 + 0.301035i
\(389\) 3.68359 3.68359i 0.186765 0.186765i −0.607531 0.794296i \(-0.707840\pi\)
0.794296 + 0.607531i \(0.207840\pi\)
\(390\) −2.43565 3.89729i −0.123334 0.197347i
\(391\) −44.1026 −2.23037
\(392\) 13.4575 + 10.8933i 0.679708 + 0.550193i
\(393\) 22.2718 1.12347
\(394\) 29.5563 18.4715i 1.48902 0.930582i
\(395\) 4.38046 + 4.38046i 0.220405 + 0.220405i
\(396\) 24.2168 8.34211i 1.21694 0.419207i
\(397\) −16.9158 + 16.9158i −0.848981 + 0.848981i −0.990006 0.141025i \(-0.954960\pi\)
0.141025 + 0.990006i \(0.454960\pi\)
\(398\) −32.6532 7.53632i −1.63676 0.377762i
\(399\) 15.1682i 0.759361i
\(400\) −8.69185 + 6.79452i −0.434592 + 0.339726i
\(401\) −6.68430 −0.333798 −0.166899 0.985974i \(-0.553375\pi\)
−0.166899 + 0.985974i \(0.553375\pi\)
\(402\) 6.62138 28.6890i 0.330245 1.43088i
\(403\) 4.57844 4.57844i 0.228068 0.228068i
\(404\) 5.00182 + 14.5201i 0.248850 + 0.722402i
\(405\) 11.0199 11.0199i 0.547582 0.547582i
\(406\) −0.357751 + 0.223581i −0.0177549 + 0.0110961i
\(407\) 45.1643 2.23871
\(408\) 3.83584 + 36.4260i 0.189902 + 1.80335i
\(409\) 10.5773i 0.523016i −0.965201 0.261508i \(-0.915780\pi\)
0.965201 0.261508i \(-0.0842198\pi\)
\(410\) −12.2988 5.70751i −0.607394 0.281874i
\(411\) 3.58992 3.58992i 0.177078 0.177078i
\(412\) −13.0278 + 26.7199i −0.641833 + 1.31640i
\(413\) 1.84116 1.84116i 0.0905975 0.0905975i
\(414\) 26.4054 + 6.09432i 1.29775 + 0.299520i
\(415\) −18.7306 −0.919450
\(416\) 4.95741 + 1.80249i 0.243057 + 0.0883744i
\(417\) 31.2833i 1.53195i
\(418\) −50.7539 11.7139i −2.48245 0.572947i
\(419\) −12.6697 12.6697i −0.618956 0.618956i 0.326307 0.945264i \(-0.394196\pi\)
−0.945264 + 0.326307i \(0.894196\pi\)
\(420\) −2.86327 + 5.87255i −0.139713 + 0.286551i
\(421\) −5.71221 5.71221i −0.278396 0.278396i 0.554072 0.832468i \(-0.313073\pi\)
−0.832468 + 0.554072i \(0.813073\pi\)
\(422\) 1.79533 1.12201i 0.0873955 0.0546188i
\(423\) −4.93012 −0.239711
\(424\) −3.46309 32.8862i −0.168182 1.59710i
\(425\) 15.3453 0.744356
\(426\) 21.1684 13.2295i 1.02561 0.640970i
\(427\) 7.10033 + 7.10033i 0.343609 + 0.343609i
\(428\) 16.1030 5.54709i 0.778367 0.268129i
\(429\) −8.13038 + 8.13038i −0.392538 + 0.392538i
\(430\) 4.44883 19.2758i 0.214542 0.929563i
\(431\) 15.7038 0.756424 0.378212 0.925719i \(-0.376539\pi\)
0.378212 + 0.925719i \(0.376539\pi\)
\(432\) −0.659608 + 5.38386i −0.0317354 + 0.259031i
\(433\) 0.791646 0.0380441 0.0190220 0.999819i \(-0.493945\pi\)
0.0190220 + 0.999819i \(0.493945\pi\)
\(434\) −8.96895 2.07002i −0.430524 0.0993642i
\(435\) 0.784236 + 0.784236i 0.0376013 + 0.0376013i
\(436\) −0.853816 + 0.294119i −0.0408904 + 0.0140857i
\(437\) −38.9690 38.9690i −1.86414 1.86414i
\(438\) 7.35717 + 11.7722i 0.351539 + 0.562498i
\(439\) 8.29052 0.395685 0.197842 0.980234i \(-0.436607\pi\)
0.197842 + 0.980234i \(0.436607\pi\)
\(440\) −17.4387 14.1159i −0.831359 0.672948i
\(441\) 14.7978i 0.704655i
\(442\) −3.88846 6.22192i −0.184955 0.295947i
\(443\) 5.00736 5.00736i 0.237907 0.237907i −0.578076 0.815983i \(-0.696196\pi\)
0.815983 + 0.578076i \(0.196196\pi\)
\(444\) 17.3922 35.6713i 0.825399 1.69289i
\(445\) 18.2932 18.2932i 0.867178 0.867178i
\(446\) 10.7556 + 2.48238i 0.509292 + 0.117544i
\(447\) 10.7360 0.507795
\(448\) −1.56201 7.33437i −0.0737982 0.346516i
\(449\) −22.7225 −1.07234 −0.536171 0.844110i \(-0.680130\pi\)
−0.536171 + 0.844110i \(0.680130\pi\)
\(450\) −9.18762 2.12049i −0.433109 0.0999608i
\(451\) −6.99394 + 33.1931i −0.329332 + 1.56300i
\(452\) 18.3280 + 8.93618i 0.862079 + 0.420323i
\(453\) −36.6763 + 36.6763i −1.72320 + 1.72320i
\(454\) −11.9228 + 7.45129i −0.559565 + 0.349707i
\(455\) 1.30874i 0.0613549i
\(456\) −28.7965 + 35.5752i −1.34852 + 1.66596i
\(457\) −36.0943 −1.68842 −0.844209 0.536014i \(-0.819929\pi\)
−0.844209 + 0.536014i \(0.819929\pi\)
\(458\) −13.0304 20.8500i −0.608872 0.974256i
\(459\) 5.33482 5.33482i 0.249008 0.249008i
\(460\) −7.73119 22.4433i −0.360469 1.04643i
\(461\) −4.68506 4.68506i −0.218205 0.218205i 0.589537 0.807742i \(-0.299310\pi\)
−0.807742 + 0.589537i \(0.799310\pi\)
\(462\) 15.9270 + 3.67594i 0.740993 + 0.171020i
\(463\) 29.5820i 1.37479i 0.726284 + 0.687395i \(0.241246\pi\)
−0.726284 + 0.687395i \(0.758754\pi\)
\(464\) −1.26352 0.154802i −0.0586576 0.00718648i
\(465\) 24.1989i 1.12219i
\(466\) −3.28653 0.758526i −0.152246 0.0351380i
\(467\) −24.0945 24.0945i −1.11496 1.11496i −0.992469 0.122492i \(-0.960911\pi\)
−0.122492 0.992469i \(-0.539089\pi\)
\(468\) 1.46834 + 4.26255i 0.0678743 + 0.197036i
\(469\) 5.92877 5.92877i 0.273765 0.273765i
\(470\) 2.28870 + 3.66215i 0.105570 + 0.168922i
\(471\) 15.3859i 0.708943i
\(472\) 7.81360 0.822812i 0.359650 0.0378730i
\(473\) −49.4935 −2.27571
\(474\) −7.21760 11.5489i −0.331515 0.530457i
\(475\) 13.5591 + 13.5591i 0.622132 + 0.622132i
\(476\) −4.57114 + 9.37538i −0.209518 + 0.429720i
\(477\) 19.9847 19.9847i 0.915034 0.915034i
\(478\) −3.00653 + 13.0266i −0.137515 + 0.595825i
\(479\) 15.5418i 0.710123i 0.934843 + 0.355062i \(0.115540\pi\)
−0.934843 + 0.355062i \(0.884460\pi\)
\(480\) −17.8643 + 8.33748i −0.815392 + 0.380552i
\(481\) 7.94964i 0.362472i
\(482\) −20.4612 4.72242i −0.931983 0.215100i
\(483\) 12.2288 + 12.2288i 0.556430 + 0.556430i
\(484\) −14.9583 + 30.6794i −0.679922 + 1.39452i
\(485\) 3.49227 + 3.49227i 0.158576 + 0.158576i
\(486\) −24.1746 + 15.1082i −1.09658 + 0.685322i
\(487\) 0.0119772i 0.000542737i −1.00000 0.000271369i \(-0.999914\pi\)
1.00000 0.000271369i \(-8.63793e-5\pi\)
\(488\) 3.17313 + 30.1327i 0.143641 + 1.36405i
\(489\) 5.86040 0.265016
\(490\) 10.9919 6.86953i 0.496565 0.310334i
\(491\) −22.5615 + 22.5615i −1.01818 + 1.01818i −0.0183528 + 0.999832i \(0.505842\pi\)
−0.999832 + 0.0183528i \(0.994158\pi\)
\(492\) 23.5231 + 18.3062i 1.06050 + 0.825307i
\(493\) 1.25201 + 1.25201i 0.0563878 + 0.0563878i
\(494\) 2.06184 8.93350i 0.0927665 0.401937i
\(495\) 19.1754i 0.861871i
\(496\) −17.1057 21.8823i −0.768068 0.982545i
\(497\) 7.10855 0.318862
\(498\) 40.1222 + 9.26014i 1.79792 + 0.414957i
\(499\) −28.4061 + 28.4061i −1.27163 + 1.27163i −0.326401 + 0.945231i \(0.605836\pi\)
−0.945231 + 0.326401i \(0.894164\pi\)
\(500\) 7.56663 + 21.9656i 0.338390 + 0.982333i
\(501\) −24.1971 + 24.1971i −1.08105 + 1.08105i
\(502\) 2.29305 1.43307i 0.102344 0.0639609i
\(503\) 3.23625 0.144297 0.0721486 0.997394i \(-0.477014\pi\)
0.0721486 + 0.997394i \(0.477014\pi\)
\(504\) 4.03239 4.98162i 0.179617 0.221899i
\(505\) 11.4973 0.511625
\(506\) −50.3623 + 31.4745i −2.23888 + 1.39921i
\(507\) 19.9645 + 19.9645i 0.886654 + 0.886654i
\(508\) −3.35893 1.63771i −0.149028 0.0726615i
\(509\) 25.9419 25.9419i 1.14985 1.14985i 0.163273 0.986581i \(-0.447795\pi\)
0.986581 0.163273i \(-0.0522051\pi\)
\(510\) 26.7187 + 6.16662i 1.18312 + 0.273063i
\(511\) 3.95321i 0.174880i
\(512\) 10.2606 20.1673i 0.453460 0.891277i
\(513\) 9.42766 0.416241
\(514\) 5.57479 24.1544i 0.245894 1.06540i
\(515\) 15.7366 + 15.7366i 0.693436 + 0.693436i
\(516\) −19.0594 + 39.0906i −0.839042 + 1.72087i
\(517\) 7.63984 7.63984i 0.336000 0.336000i
\(518\) 9.58360 5.98938i 0.421079 0.263158i
\(519\) −10.9355 −0.480014
\(520\) 2.48462 3.06950i 0.108958 0.134606i
\(521\) 39.7509 1.74152 0.870760 0.491709i \(-0.163628\pi\)
0.870760 + 0.491709i \(0.163628\pi\)
\(522\) −0.576603 0.922622i −0.0252372 0.0403821i
\(523\) −3.27122 + 3.27122i −0.143041 + 0.143041i −0.775001 0.631960i \(-0.782251\pi\)
0.631960 + 0.775001i \(0.282251\pi\)
\(524\) 6.23304 + 18.0943i 0.272291 + 0.790452i
\(525\) −4.25496 4.25496i −0.185702 0.185702i
\(526\) −12.8649 2.96919i −0.560935 0.129463i
\(527\) 38.6328i 1.68287i
\(528\) 30.3762 + 38.8586i 1.32195 + 1.69110i
\(529\) −39.8345 −1.73194
\(530\) −24.1222 5.56738i −1.04780 0.241831i
\(531\) 4.74825 + 4.74825i 0.206057 + 0.206057i
\(532\) −12.3231 + 4.24501i −0.534274 + 0.184044i
\(533\) −5.84253 1.23105i −0.253068 0.0533225i
\(534\) −48.2290 + 30.1412i −2.08707 + 1.30434i
\(535\) 12.7507i 0.551261i
\(536\) 25.1608 2.64956i 1.08678 0.114444i
\(537\) 35.3178i 1.52408i
\(538\) 1.90030 + 3.04066i 0.0819276 + 0.131092i
\(539\) −22.9310 22.9310i −0.987706 0.987706i
\(540\) 3.65002 + 1.77964i 0.157072 + 0.0765834i
\(541\) −4.10820 4.10820i −0.176625 0.176625i 0.613258 0.789883i \(-0.289859\pi\)
−0.789883 + 0.613258i \(0.789859\pi\)
\(542\) 34.4585 + 7.95297i 1.48012 + 0.341609i
\(543\) −11.3830 −0.488493
\(544\) −28.5200 + 13.3106i −1.22278 + 0.570686i
\(545\) 0.676071i 0.0289597i
\(546\) −0.647024 + 2.80341i −0.0276901 + 0.119975i
\(547\) 0.684008 0.684008i 0.0292461 0.0292461i −0.692333 0.721579i \(-0.743417\pi\)
0.721579 + 0.692333i \(0.243417\pi\)
\(548\) 3.92123 + 1.91187i 0.167507 + 0.0816710i
\(549\) −18.3114 + 18.3114i −0.781511 + 0.781511i
\(550\) 17.5233 10.9514i 0.747197 0.466969i
\(551\) 2.21255i 0.0942578i
\(552\) 5.46504 + 51.8973i 0.232608 + 2.20890i
\(553\) 3.87821i 0.164918i
\(554\) 0.416210 0.260115i 0.0176831 0.0110512i
\(555\) −21.0085 21.0085i −0.891760 0.891760i
\(556\) −25.4154 + 8.75499i −1.07785 + 0.371294i
\(557\) 8.89809 8.89809i 0.377024 0.377024i −0.493003 0.870027i \(-0.664101\pi\)
0.870027 + 0.493003i \(0.164101\pi\)
\(558\) 5.33848 23.1305i 0.225996 0.979191i
\(559\) 8.71165i 0.368464i
\(560\) −5.57235 0.682700i −0.235475 0.0288494i
\(561\) 68.6041i 2.89647i
\(562\) 24.9390 + 5.75588i 1.05199 + 0.242797i
\(563\) 2.97907 2.97907i 0.125553 0.125553i −0.641538 0.767091i \(-0.721703\pi\)
0.767091 + 0.641538i \(0.221703\pi\)
\(564\) −3.09203 8.97606i −0.130198 0.377960i
\(565\) 10.7942 10.7942i 0.454116 0.454116i
\(566\) 9.89619 6.18473i 0.415968 0.259964i
\(567\) −9.75637 −0.409729
\(568\) 16.6722 + 13.4954i 0.699551 + 0.566255i
\(569\) 14.8051i 0.620662i −0.950629 0.310331i \(-0.899560\pi\)
0.950629 0.310331i \(-0.100440\pi\)
\(570\) 18.1597 + 29.0573i 0.760626 + 1.21708i
\(571\) −5.84075 5.84075i −0.244428 0.244428i 0.574251 0.818679i \(-0.305293\pi\)
−0.818679 + 0.574251i \(0.805293\pi\)
\(572\) −8.88073 4.32997i −0.371322 0.181045i
\(573\) 25.8730 + 25.8730i 1.08086 + 1.08086i
\(574\) 2.91777 + 7.97088i 0.121786 + 0.332698i
\(575\) 21.8630 0.911748
\(576\) 18.9150 4.02835i 0.788123 0.167848i
\(577\) 5.62772i 0.234285i 0.993115 + 0.117143i \(0.0373735\pi\)
−0.993115 + 0.117143i \(0.962627\pi\)
\(578\) 19.2298 + 4.43822i 0.799856 + 0.184605i
\(579\) 1.60846 + 1.60846i 0.0668452 + 0.0668452i
\(580\) −0.417658 + 0.856614i −0.0173423 + 0.0355689i
\(581\) 8.29152 + 8.29152i 0.343990 + 0.343990i
\(582\) −5.75414 9.20720i −0.238517 0.381651i
\(583\) 61.9374i 2.56519i
\(584\) −7.50508 + 9.27177i −0.310562 + 0.383668i
\(585\) 3.37518 0.139547
\(586\) 13.7400 + 21.9853i 0.567593 + 0.908205i
\(587\) −25.7631 25.7631i −1.06336 1.06336i −0.997852 0.0655047i \(-0.979134\pi\)
−0.0655047 0.997852i \(-0.520866\pi\)
\(588\) −26.9416 + 9.28073i −1.11105 + 0.382731i
\(589\) −34.1359 + 34.1359i −1.40654 + 1.40654i
\(590\) 1.32278 5.73132i 0.0544580 0.235955i
\(591\) 57.3624i 2.35957i
\(592\) 33.8478 + 4.14689i 1.39114 + 0.170436i
\(593\) 23.5534i 0.967223i −0.875283 0.483611i \(-0.839325\pi\)
0.875283 0.483611i \(-0.160675\pi\)
\(594\) 2.28474 9.89928i 0.0937440 0.406173i
\(595\) 5.52158 + 5.52158i 0.226363 + 0.226363i
\(596\) 3.00459 + 8.72222i 0.123073 + 0.357276i
\(597\) 38.9997 38.9997i 1.59615 1.59615i
\(598\) −5.54002 8.86458i −0.226548 0.362500i
\(599\) 23.8080i 0.972770i −0.873745 0.486385i \(-0.838315\pi\)
0.873745 0.486385i \(-0.161685\pi\)
\(600\) −1.90154 18.0574i −0.0776298 0.737190i
\(601\) 16.1268 0.657826 0.328913 0.944360i \(-0.393318\pi\)
0.328913 + 0.944360i \(0.393318\pi\)
\(602\) −10.5022 + 6.56349i −0.428039 + 0.267508i
\(603\) 15.2900 + 15.2900i 0.622657 + 0.622657i
\(604\) −40.0612 19.5326i −1.63007 0.794769i
\(605\) 18.0685 + 18.0685i 0.734587 + 0.734587i
\(606\) −24.6281 5.68412i −1.00045 0.230902i
\(607\) 43.9405 1.78349 0.891745 0.452539i \(-0.149482\pi\)
0.891745 + 0.452539i \(0.149482\pi\)
\(608\) −36.9613 13.4390i −1.49898 0.545022i
\(609\) 0.694319i 0.0281352i
\(610\) 22.1025 + 5.10123i 0.894906 + 0.206543i
\(611\) 1.34473 + 1.34473i 0.0544021 + 0.0544021i
\(612\) −24.1786 11.7887i −0.977362 0.476531i
\(613\) −22.3145 + 22.3145i −0.901273 + 0.901273i −0.995546 0.0942730i \(-0.969947\pi\)
0.0942730 + 0.995546i \(0.469947\pi\)
\(614\) −16.0754 25.7223i −0.648752 1.03807i
\(615\) 18.6933 12.1867i 0.753787 0.491417i
\(616\) 1.47093 + 13.9683i 0.0592657 + 0.562800i
\(617\) 0.295335i 0.0118898i 0.999982 + 0.00594488i \(0.00189232\pi\)
−0.999982 + 0.00594488i \(0.998108\pi\)
\(618\) −25.9288 41.4887i −1.04301 1.66892i
\(619\) 12.9261 12.9261i 0.519545 0.519545i −0.397889 0.917434i \(-0.630257\pi\)
0.917434 + 0.397889i \(0.130257\pi\)
\(620\) −19.6598 + 6.77233i −0.789558 + 0.271983i
\(621\) 7.60069 7.60069i 0.305005 0.305005i
\(622\) 13.9328 + 3.21567i 0.558655 + 0.128937i
\(623\) −16.1957 −0.648868
\(624\) −6.83973 + 5.34670i −0.273808 + 0.214039i
\(625\) 3.60240 0.144096
\(626\) 11.0418 + 2.54842i 0.441318 + 0.101855i
\(627\) 60.6183 60.6183i 2.42086 2.42086i
\(628\) 12.4999 4.30591i 0.498800 0.171825i
\(629\) −33.5395 33.5395i −1.33731 1.33731i
\(630\) −2.54291 4.06891i −0.101312 0.162109i
\(631\) 31.7399i 1.26355i −0.775153 0.631773i \(-0.782327\pi\)
0.775153 0.631773i \(-0.217673\pi\)
\(632\) 7.36270 9.09587i 0.292872 0.361814i
\(633\) 3.48436i 0.138491i
\(634\) 9.32972 5.83072i 0.370531 0.231567i
\(635\) −1.97822 + 1.97822i −0.0785034 + 0.0785034i
\(636\) 48.9190 + 23.8514i 1.93976 + 0.945768i
\(637\) 4.03622 4.03622i 0.159921 0.159921i
\(638\) 2.32323 + 0.536199i 0.0919778 + 0.0212283i
\(639\) 18.3326i 0.725226i
\(640\) −11.7732 12.1802i −0.465375 0.481463i
\(641\) 22.1375i 0.874379i −0.899369 0.437190i \(-0.855974\pi\)
0.899369 0.437190i \(-0.144026\pi\)
\(642\) −6.30376 + 27.3129i −0.248790 + 1.07795i
\(643\) −11.9706 + 11.9706i −0.472076 + 0.472076i −0.902586 0.430510i \(-0.858334\pi\)
0.430510 + 0.902586i \(0.358334\pi\)
\(644\) −6.51266 + 13.3574i −0.256635 + 0.526356i
\(645\) 23.0222 + 23.0222i 0.906500 + 0.906500i
\(646\) 28.9915 + 46.3893i 1.14066 + 1.82516i
\(647\) 22.5965i 0.888362i 0.895937 + 0.444181i \(0.146505\pi\)
−0.895937 + 0.444181i \(0.853495\pi\)
\(648\) −22.8824 18.5222i −0.898904 0.727623i
\(649\) −14.7160 −0.577654
\(650\) 1.92762 + 3.08439i 0.0756076 + 0.120980i
\(651\) 10.7121 10.7121i 0.419842 0.419842i
\(652\) 1.64010 + 4.76115i 0.0642313 + 0.186461i
\(653\) 8.76576 8.76576i 0.343031 0.343031i −0.514475 0.857505i \(-0.672013\pi\)
0.857505 + 0.514475i \(0.172013\pi\)
\(654\) 0.334240 1.44819i 0.0130698 0.0566286i
\(655\) 14.3275 0.559820
\(656\) −8.28925 + 24.2340i −0.323641 + 0.946180i
\(657\) −10.1951 −0.397750
\(658\) 0.607986 2.63427i 0.0237018 0.102695i
\(659\) −11.9930 + 11.9930i −0.467180 + 0.467180i −0.901000 0.433820i \(-0.857165\pi\)
0.433820 + 0.901000i \(0.357165\pi\)
\(660\) 34.9119 12.0263i 1.35894 0.468123i
\(661\) 14.2297 14.2297i 0.553472 0.553472i −0.373969 0.927441i \(-0.622003\pi\)
0.927441 + 0.373969i \(0.122003\pi\)
\(662\) 20.5644 + 32.9051i 0.799258 + 1.27889i
\(663\) 12.0754 0.468970
\(664\) 3.70547 + 35.1880i 0.143800 + 1.36556i
\(665\) 9.75771i 0.378388i
\(666\) 15.4463 + 24.7156i 0.598532 + 0.957710i
\(667\) 1.78379 + 1.78379i 0.0690684 + 0.0690684i
\(668\) −26.4302 12.8866i −1.02262 0.498596i
\(669\) −12.8460 + 12.8460i −0.496657 + 0.496657i
\(670\) 4.25953 18.4556i 0.164560 0.713003i
\(671\) 56.7515i 2.19087i
\(672\) 11.5988 + 4.21727i 0.447434 + 0.162685i
\(673\) 14.3662i 0.553774i −0.960902 0.276887i \(-0.910697\pi\)
0.960902 0.276887i \(-0.0893028\pi\)
\(674\) −9.19821 2.12293i −0.354302 0.0817723i
\(675\) −2.64462 + 2.64462i −0.101792 + 0.101792i
\(676\) −10.6324 + 21.8070i −0.408939 + 0.838731i
\(677\) −6.95122 + 6.95122i −0.267157 + 0.267157i −0.827954 0.560796i \(-0.810495\pi\)
0.560796 + 0.827954i \(0.310495\pi\)
\(678\) −28.4584 + 17.7854i −1.09294 + 0.683045i
\(679\) 3.09186i 0.118655i
\(680\) 2.46759 + 23.4328i 0.0946278 + 0.898606i
\(681\) 23.1396i 0.886712i
\(682\) 27.5709 + 44.1162i 1.05574 + 1.68930i
\(683\) −12.6712 12.6712i −0.484849 0.484849i 0.421827 0.906676i \(-0.361389\pi\)
−0.906676 + 0.421827i \(0.861389\pi\)
\(684\) −10.9477 31.7806i −0.418594 1.21516i
\(685\) 2.30939 2.30939i 0.0882373 0.0882373i
\(686\) −16.9484 3.91167i −0.647094 0.149348i
\(687\) 40.4654 1.54385
\(688\) −37.0923 4.54439i −1.41413 0.173253i
\(689\) −10.9020 −0.415332
\(690\) 38.0670 + 8.78580i 1.44918 + 0.334470i
\(691\) 6.98178 6.98178i 0.265599 0.265599i −0.561725 0.827324i \(-0.689862\pi\)
0.827324 + 0.561725i \(0.189862\pi\)
\(692\) −3.06042 8.88429i −0.116340 0.337730i
\(693\) −8.48842 + 8.48842i −0.322448 + 0.322448i
\(694\) 6.12023 + 9.79297i 0.232321 + 0.371736i
\(695\) 20.1245i 0.763366i
\(696\) 1.31815 1.62844i 0.0499643 0.0617258i
\(697\) 29.8434 19.4558i 1.13040 0.736941i
\(698\) −10.6469 17.0362i −0.402993 0.644828i
\(699\) 3.92530 3.92530i 0.148468 0.148468i
\(700\) 2.26605 4.64765i 0.0856485 0.175665i
\(701\) −10.4092 10.4092i −0.393151 0.393151i 0.482658 0.875809i \(-0.339672\pi\)
−0.875809 + 0.482658i \(0.839672\pi\)
\(702\) 1.74243 + 0.402151i 0.0657639 + 0.0151782i
\(703\) 59.2708i 2.23544i
\(704\) −23.0686 + 35.5535i −0.869432 + 1.33997i
\(705\) −7.10745 −0.267682
\(706\) 13.2417 + 3.05617i 0.498359 + 0.115021i
\(707\) −5.08955 5.08955i −0.191412 0.191412i
\(708\) −5.66696 + 11.6229i −0.212978 + 0.436815i
\(709\) 31.3121 + 31.3121i 1.17595 + 1.17595i 0.980767 + 0.195183i \(0.0625302\pi\)
0.195183 + 0.980767i \(0.437470\pi\)
\(710\) 13.6176 8.51050i 0.511061 0.319393i
\(711\) 10.0017 0.375094
\(712\) −37.9850 30.7472i −1.42355 1.15230i
\(713\) 55.0415i 2.06132i
\(714\) −9.09780 14.5574i −0.340477 0.544796i
\(715\) −5.23027 + 5.23027i −0.195601 + 0.195601i
\(716\) 28.6932 9.88411i 1.07232 0.369387i
\(717\) −15.5585 15.5585i −0.581042 0.581042i
\(718\) 7.72406 33.4667i 0.288259 1.24897i
\(719\) 8.51497i 0.317555i −0.987314 0.158777i \(-0.949245\pi\)
0.987314 0.158777i \(-0.0507552\pi\)
\(720\) 1.76065 14.3708i 0.0656155 0.535568i
\(721\) 13.9323i 0.518865i
\(722\) −9.32990 + 40.4244i −0.347223 + 1.50444i
\(723\) 24.4380 24.4380i 0.908860 0.908860i
\(724\) −3.18568 9.24791i −0.118395 0.343696i
\(725\) −0.620659 0.620659i −0.0230507 0.0230507i
\(726\) −29.7710 47.6366i −1.10491 1.76796i
\(727\) 22.1331 0.820870 0.410435 0.911890i \(-0.365377\pi\)
0.410435 + 0.911890i \(0.365377\pi\)
\(728\) −2.45865 + 0.258908i −0.0911236 + 0.00959578i
\(729\) 15.6926i 0.581207i
\(730\) 4.73286 + 7.57305i 0.175171 + 0.280291i
\(731\) 36.7544 + 36.7544i 1.35941 + 1.35941i
\(732\) −44.8231 21.8543i −1.65671 0.807760i
\(733\) −10.6124 10.6124i −0.391980 0.391980i 0.483413 0.875392i \(-0.339397\pi\)
−0.875392 + 0.483413i \(0.839397\pi\)
\(734\) −32.9907 7.61420i −1.21771 0.281045i
\(735\) 21.3330i 0.786879i
\(736\) −40.6334 + 18.9640i −1.49777 + 0.699023i
\(737\) −47.3875 −1.74554
\(738\) −20.5565 + 7.52479i −0.756695 + 0.276991i
\(739\) 10.6853 + 10.6853i 0.393064 + 0.393064i 0.875778 0.482714i \(-0.160349\pi\)
−0.482714 + 0.875778i \(0.660349\pi\)
\(740\) 11.1884 22.9473i 0.411294 0.843561i
\(741\) 10.6698 + 10.6698i 0.391965 + 0.391965i
\(742\) 8.21371 + 13.1428i 0.301535 + 0.482486i
\(743\) 22.9489i 0.841915i −0.907080 0.420957i \(-0.861694\pi\)
0.907080 0.420957i \(-0.138306\pi\)
\(744\) 45.4608 4.78725i 1.66667 0.175509i
\(745\) 6.90645 0.253033
\(746\) −22.2269 + 13.8910i −0.813785 + 0.508584i
\(747\) −21.3834 + 21.3834i −0.782377 + 0.782377i
\(748\) 55.7359 19.1997i 2.03791 0.702009i
\(749\) −5.64438 + 5.64438i −0.206241 + 0.206241i
\(750\) −37.2567 8.59879i −1.36042 0.313983i
\(751\) 41.2205i 1.50416i −0.659073 0.752079i \(-0.729051\pi\)
0.659073 0.752079i \(-0.270949\pi\)
\(752\) 6.42706 5.02411i 0.234371 0.183210i
\(753\) 4.45032i 0.162179i
\(754\) −0.0943797 + 0.408927i −0.00343710 + 0.0148922i
\(755\) −23.5938 + 23.5938i −0.858668 + 0.858668i
\(756\) −0.827967 2.40356i −0.0301129 0.0874165i
\(757\) 0.113162 + 0.113162i 0.00411293 + 0.00411293i 0.709160 0.705047i \(-0.249074\pi\)
−0.705047 + 0.709160i \(0.749074\pi\)
\(758\) −19.1884 + 11.9920i −0.696955 + 0.435570i
\(759\) 97.7425i 3.54783i
\(760\) −18.5248 + 22.8855i −0.671965 + 0.830144i
\(761\) 7.99101i 0.289674i −0.989456 0.144837i \(-0.953734\pi\)
0.989456 0.144837i \(-0.0462658\pi\)
\(762\) 5.21549 3.25948i 0.188937 0.118078i
\(763\) 0.299278 0.299278i 0.0108346 0.0108346i
\(764\) −13.7791 + 28.2608i −0.498510 + 1.02244i
\(765\) −14.2399 + 14.2399i −0.514844 + 0.514844i
\(766\) 1.24403 5.39012i 0.0449487 0.194753i
\(767\) 2.59026i 0.0935287i
\(768\) 19.1972 + 31.9112i 0.692718 + 1.15149i
\(769\) 39.4719 1.42339 0.711697 0.702487i \(-0.247927\pi\)
0.711697 + 0.702487i \(0.247927\pi\)
\(770\) 10.2458 + 2.36473i 0.369235 + 0.0852188i
\(771\) 28.8490 + 28.8490i 1.03897 + 1.03897i
\(772\) −0.856611 + 1.75690i −0.0308301 + 0.0632323i
\(773\) 13.5577 + 13.5577i 0.487638 + 0.487638i 0.907560 0.419922i \(-0.137943\pi\)
−0.419922 + 0.907560i \(0.637943\pi\)
\(774\) −16.9269 27.0847i −0.608425 0.973540i
\(775\) 19.1514i 0.687939i
\(776\) 5.86982 7.25157i 0.210714 0.260316i
\(777\) 18.5997i 0.667261i
\(778\) −6.24746 + 3.90442i −0.223982 + 0.139980i
\(779\) 43.5606 + 9.17841i 1.56072 + 0.328851i
\(780\) 2.11682 + 6.14505i 0.0757943 + 0.220028i
\(781\) −28.4086 28.4086i −1.01654 1.01654i
\(782\) 60.7729 + 14.0263i 2.17324 + 0.501579i
\(783\) −0.431546 −0.0154222
\(784\) −15.0799 19.2908i −0.538566 0.688957i
\(785\) 9.89771i 0.353264i
\(786\) −30.6903 7.08328i −1.09469 0.252652i
\(787\) −11.7589 11.7589i −0.419161 0.419161i 0.465754 0.884914i \(-0.345783\pi\)
−0.884914 + 0.465754i \(0.845783\pi\)
\(788\) −46.6028 + 16.0535i −1.66016 + 0.571884i
\(789\) 15.3653 15.3653i 0.547018 0.547018i
\(790\) −4.64307 7.42938i −0.165193 0.264325i
\(791\) −9.55659 −0.339793
\(792\) −36.0236 + 3.79347i −1.28004 + 0.134795i
\(793\) 9.98918 0.354726
\(794\) 28.6897 17.9299i 1.01816 0.636310i
\(795\) 28.8106 28.8106i 1.02181 1.02181i
\(796\) 42.5990 + 20.7699i 1.50988 + 0.736170i
\(797\) 14.3091 + 14.3091i 0.506855 + 0.506855i 0.913560 0.406705i \(-0.133322\pi\)
−0.406705 + 0.913560i \(0.633322\pi\)
\(798\) 4.82407 20.9016i 0.170770 0.739910i
\(799\) −11.3469 −0.401423
\(800\) 14.1382 6.59844i 0.499860 0.233290i
\(801\) 41.7679i 1.47580i
\(802\) 9.21088 + 2.12586i 0.325248 + 0.0750667i
\(803\) 15.7986 15.7986i 0.557521 0.557521i
\(804\) −18.2484 + 37.4273i −0.643571 + 1.31996i
\(805\) 7.86679 + 7.86679i 0.277268 + 0.277268i
\(806\) −7.76516 + 4.85292i −0.273516 + 0.170937i
\(807\) −5.90128 −0.207735
\(808\) −2.27451 21.5993i −0.0800171 0.759861i
\(809\) 31.5131 1.10794 0.553971 0.832536i \(-0.313112\pi\)
0.553971 + 0.832536i \(0.313112\pi\)
\(810\) −18.6900 + 11.6805i −0.656699 + 0.410412i
\(811\) 12.8787 12.8787i 0.452233 0.452233i −0.443862 0.896095i \(-0.646392\pi\)
0.896095 + 0.443862i \(0.146392\pi\)
\(812\) 0.564084 0.194313i 0.0197955 0.00681906i
\(813\) −41.1558 + 41.1558i −1.44340 + 1.44340i
\(814\) −62.2358 14.3639i −2.18137 0.503456i
\(815\) 3.76999 0.132057
\(816\) 6.29909 51.4145i 0.220512 1.79987i
\(817\) 64.9522i 2.27239i
\(818\) −3.36399 + 14.5755i −0.117619 + 0.509619i
\(819\) −1.49410 1.49410i −0.0522080 0.0522080i
\(820\) 15.1324 + 11.7764i 0.528446 + 0.411248i
\(821\) −32.5326 + 32.5326i −1.13540 + 1.13540i −0.146131 + 0.989265i \(0.546682\pi\)
−0.989265 + 0.146131i \(0.953318\pi\)
\(822\) −6.08859 + 3.80514i −0.212364 + 0.132719i
\(823\) 8.75230 0.305086 0.152543 0.988297i \(-0.451254\pi\)
0.152543 + 0.988297i \(0.451254\pi\)
\(824\) 26.4501 32.6764i 0.921432 1.13834i
\(825\) 34.0090i 1.18404i
\(826\) −3.12265 + 1.95154i −0.108651 + 0.0679027i
\(827\) −32.6689 32.6689i −1.13601 1.13601i −0.989159 0.146850i \(-0.953087\pi\)
−0.146850 0.989159i \(-0.546913\pi\)
\(828\) −34.4481 16.7958i −1.19715 0.583695i
\(829\) −31.8076 31.8076i −1.10472 1.10472i −0.993833 0.110890i \(-0.964630\pi\)
−0.110890 0.993833i \(-0.535370\pi\)
\(830\) 25.8106 + 5.95704i 0.895898 + 0.206772i
\(831\) 0.807775i 0.0280214i
\(832\) −6.25799 4.06045i −0.216957 0.140771i
\(833\) 34.0576i 1.18002i
\(834\) 9.94925 43.1080i 0.344514 1.49271i
\(835\) −15.5660 + 15.5660i −0.538682 + 0.538682i
\(836\) 66.2128 + 32.2833i 2.29002 + 1.11654i
\(837\) −6.65802 6.65802i −0.230135 0.230135i
\(838\) 13.4293 + 21.4882i 0.463907 + 0.742297i
\(839\) −50.9883 −1.76031 −0.880155 0.474686i \(-0.842562\pi\)
−0.880155 + 0.474686i \(0.842562\pi\)
\(840\) 5.81325 7.18168i 0.200576 0.247791i
\(841\) 28.8987i 0.996508i
\(842\) 6.05466 + 9.68806i 0.208657 + 0.333872i
\(843\) −29.7861 + 29.7861i −1.02589 + 1.02589i
\(844\) −2.83079 + 0.975139i −0.0974399 + 0.0335657i
\(845\) 12.8431 + 12.8431i 0.441817 + 0.441817i
\(846\) 6.79365 + 1.56796i 0.233571 + 0.0539077i
\(847\) 15.9968i 0.549656i
\(848\) −5.68697 + 46.4182i −0.195291 + 1.59401i
\(849\) 19.2064i 0.659161i
\(850\) −21.1456 4.88038i −0.725289 0.167396i
\(851\) −47.7848 47.7848i −1.63804 1.63804i
\(852\) −33.3773 + 11.4977i −1.14349 + 0.393904i
\(853\) 24.8028 24.8028i 0.849231 0.849231i −0.140806 0.990037i \(-0.544969\pi\)
0.990037 + 0.140806i \(0.0449694\pi\)
\(854\) −7.52600 12.0423i −0.257534 0.412080i
\(855\) −25.1646 −0.860612
\(856\) −23.9539 + 2.52247i −0.818728 + 0.0862162i
\(857\) 26.6469i 0.910240i −0.890430 0.455120i \(-0.849596\pi\)
0.890430 0.455120i \(-0.150404\pi\)
\(858\) 13.7893 8.61780i 0.470760 0.294207i
\(859\) −22.9697 + 22.9697i −0.783716 + 0.783716i −0.980456 0.196740i \(-0.936965\pi\)
0.196740 + 0.980456i \(0.436965\pi\)
\(860\) −12.2609 + 25.1470i −0.418092 + 0.857505i
\(861\) −13.6697 2.88027i −0.465863 0.0981594i
\(862\) −21.6396 4.99439i −0.737048 0.170110i
\(863\) −41.4358 −1.41049 −0.705246 0.708962i \(-0.749164\pi\)
−0.705246 + 0.708962i \(0.749164\pi\)
\(864\) 2.62120 7.20912i 0.0891751 0.245259i
\(865\) −7.03478 −0.239190
\(866\) −1.09088 0.251773i −0.0370696 0.00855560i
\(867\) −22.9673 + 22.9673i −0.780011 + 0.780011i
\(868\) 11.7008 + 5.70493i 0.397150 + 0.193638i
\(869\) −15.4989 + 15.4989i −0.525764 + 0.525764i
\(870\) −0.831252 1.33009i −0.0281821 0.0450941i
\(871\) 8.34097i 0.282623i
\(872\) 1.27009 0.133747i 0.0430107 0.00452924i
\(873\) 7.97375 0.269870
\(874\) 41.3052 + 66.0924i 1.39717 + 2.23561i
\(875\) −7.69934 7.69934i −0.260285 0.260285i
\(876\) −6.39410 18.5618i −0.216036 0.627146i
\(877\) −7.14373 7.14373i −0.241227 0.241227i 0.576131 0.817358i \(-0.304562\pi\)
−0.817358 + 0.576131i \(0.804562\pi\)
\(878\) −11.4242 2.63670i −0.385549 0.0889842i
\(879\) −42.6688 −1.43918
\(880\) 19.5410 + 24.9977i 0.658727 + 0.842671i
\(881\) −26.6637 −0.898324 −0.449162 0.893450i \(-0.648277\pi\)
−0.449162 + 0.893450i \(0.648277\pi\)
\(882\) 4.70624 20.3911i 0.158467 0.686605i
\(883\) −10.5647 + 10.5647i −0.355529 + 0.355529i −0.862162 0.506633i \(-0.830890\pi\)
0.506633 + 0.862162i \(0.330890\pi\)
\(884\) 3.37945 + 9.81041i 0.113663 + 0.329960i
\(885\) 6.84526 + 6.84526i 0.230101 + 0.230101i
\(886\) −8.49262 + 5.30756i −0.285315 + 0.178311i
\(887\) 15.9407 0.535237 0.267618 0.963525i \(-0.413763\pi\)
0.267618 + 0.963525i \(0.413763\pi\)
\(888\) −35.3111 + 43.6233i −1.18496 + 1.46390i
\(889\) 1.75141 0.0587403
\(890\) −31.0257 + 19.3898i −1.03998 + 0.649949i
\(891\) 38.9904 + 38.9904i 1.30623 + 1.30623i
\(892\) −14.0316 6.84137i −0.469813 0.229066i
\(893\) −10.0260 10.0260i −0.335509 0.335509i
\(894\) −14.7941 3.41445i −0.494788 0.114196i
\(895\) 22.7199i 0.759444i
\(896\) −0.180169 + 10.6035i −0.00601903 + 0.354237i
\(897\) 17.2043 0.574433
\(898\) 31.3113 + 7.22661i 1.04487 + 0.241155i
\(899\) 1.56255 1.56255i 0.0521141 0.0521141i
\(900\) 11.9860 + 5.84402i 0.399535 + 0.194801i
\(901\) 45.9954 45.9954i 1.53233 1.53233i
\(902\) 20.1942 43.5154i 0.672395 1.44891i
\(903\) 20.3826i 0.678290i
\(904\) −22.4138 18.1430i −0.745472 0.603426i
\(905\) −7.32270 −0.243415
\(906\) 62.2040 38.8751i 2.06659 1.29154i
\(907\) −22.4952 + 22.4952i −0.746942 + 0.746942i −0.973904 0.226962i \(-0.927121\pi\)
0.226962 + 0.973904i \(0.427121\pi\)
\(908\) 18.7993 6.47590i 0.623876 0.214910i
\(909\) 13.1257 13.1257i 0.435352 0.435352i
\(910\) −0.416230 + 1.80343i −0.0137979 + 0.0597833i
\(911\) −14.8160 −0.490875 −0.245437 0.969412i \(-0.578932\pi\)
−0.245437 + 0.969412i \(0.578932\pi\)
\(912\) 50.9955 39.8638i 1.68863 1.32002i
\(913\) 66.2724i 2.19330i
\(914\) 49.7375 + 11.4793i 1.64517 + 0.379702i
\(915\) −26.3984 + 26.3984i −0.872703 + 0.872703i
\(916\) 11.3247 + 32.8752i 0.374179 + 1.08623i
\(917\) −6.34236 6.34236i −0.209443 0.209443i
\(918\) −9.04799 + 5.65464i −0.298628 + 0.186631i
\(919\) −28.0881 −0.926541 −0.463270 0.886217i \(-0.653324\pi\)
−0.463270 + 0.886217i \(0.653324\pi\)
\(920\) 3.51566 + 33.3855i 0.115908 + 1.10069i
\(921\) 49.9215 1.64497
\(922\) 4.96593 + 7.94598i 0.163544 + 0.261687i
\(923\) 5.00038 5.00038i 0.164589 0.164589i
\(924\) −20.7782 10.1308i −0.683552 0.333279i
\(925\) 16.6265 + 16.6265i 0.546676 + 0.546676i
\(926\) 9.40818 40.7636i 0.309172 1.33958i
\(927\) 35.9306 1.18012
\(928\) 1.69189 + 0.615163i 0.0555389 + 0.0201937i
\(929\) 36.2397i 1.18899i −0.804101 0.594493i \(-0.797353\pi\)
0.804101 0.594493i \(-0.202647\pi\)
\(930\) 7.69615 33.3457i 0.252367 1.09345i
\(931\) −30.0932 + 30.0932i −0.986263 + 0.986263i
\(932\) 4.28756 + 2.09048i 0.140444 + 0.0684760i
\(933\) −16.6408 + 16.6408i −0.544795 + 0.544795i
\(934\) 25.5390 + 40.8649i 0.835662 + 1.33714i
\(935\) 44.1329i 1.44330i
\(936\) −0.667711 6.34073i −0.0218248 0.207253i
\(937\) 21.9887 0.718339 0.359169 0.933272i \(-0.383060\pi\)
0.359169 + 0.933272i \(0.383060\pi\)
\(938\) −10.0554 + 6.28421i −0.328319 + 0.205187i
\(939\) −13.1878 + 13.1878i −0.430368 + 0.430368i
\(940\) −1.98910 5.77429i −0.0648774 0.188337i
\(941\) −7.24009 7.24009i −0.236020 0.236020i 0.579180 0.815200i \(-0.303373\pi\)
−0.815200 + 0.579180i \(0.803373\pi\)
\(942\) −4.89328 + 21.2015i −0.159432 + 0.690783i
\(943\) 42.5189 27.7193i 1.38460 0.902666i
\(944\) −11.0287 1.35120i −0.358955 0.0439777i
\(945\) −1.90319 −0.0619108
\(946\) 68.2015 + 15.7408i 2.21742 + 0.511777i
\(947\) −1.15645 1.15645i −0.0375797 0.0375797i 0.688067 0.725647i \(-0.258459\pi\)
−0.725647 + 0.688067i \(0.758459\pi\)
\(948\) 6.27279 + 18.2097i 0.203731 + 0.591423i
\(949\) 2.78081 + 2.78081i 0.0902690 + 0.0902690i
\(950\) −14.3719 22.9965i −0.466287 0.746105i
\(951\) 18.1070i 0.587160i
\(952\) 9.28070 11.4654i 0.300789 0.371595i
\(953\) 36.0048i 1.16631i 0.812360 + 0.583156i \(0.198182\pi\)
−0.812360 + 0.583156i \(0.801818\pi\)
\(954\) −33.8945 + 21.1827i −1.09737 + 0.685817i
\(955\) 16.6441 + 16.6441i 0.538590 + 0.538590i
\(956\) 8.28592 16.9944i 0.267986 0.549637i
\(957\) −2.77478 + 2.77478i −0.0896957 + 0.0896957i
\(958\) 4.94288 21.4164i 0.159697 0.691933i
\(959\) −2.04460 −0.0660237
\(960\) 27.2685 5.80742i 0.880087 0.187434i
\(961\) 17.2150 0.555324
\(962\) 2.52828 10.9545i 0.0815152 0.353188i
\(963\) −14.5566 14.5566i −0.469079 0.469079i
\(964\) 26.6934 + 13.0149i 0.859737 + 0.419181i
\(965\) 1.03472 + 1.03472i 0.0333088 + 0.0333088i
\(966\) −12.9619 20.7404i −0.417044 0.667311i
\(967\) 0.929058 0.0298765 0.0149382 0.999888i \(-0.495245\pi\)
0.0149382 + 0.999888i \(0.495245\pi\)
\(968\) 30.3695 37.5185i 0.976114 1.20589i
\(969\) −90.0317 −2.89223
\(970\) −3.70164 5.92298i −0.118852 0.190176i
\(971\) 11.7842 + 11.7842i 0.378172 + 0.378172i 0.870442 0.492270i \(-0.163833\pi\)
−0.492270 + 0.870442i \(0.663833\pi\)
\(972\) 38.1173 13.1305i 1.22261 0.421160i
\(973\) 8.90854 8.90854i 0.285595 0.285595i
\(974\) −0.00380919 + 0.0165044i −0.000122054 + 0.000528835i
\(975\) −5.98613 −0.191710
\(976\) 5.21081 42.5317i 0.166794 1.36141i
\(977\) 35.8378i 1.14655i 0.819362 + 0.573277i \(0.194328\pi\)
−0.819362 + 0.573277i \(0.805672\pi\)
\(978\) −8.07556 1.86383i −0.258228 0.0595986i
\(979\) 64.7246 + 64.7246i 2.06861 + 2.06861i
\(980\) −17.3315 + 5.97029i −0.553635 + 0.190714i
\(981\) 0.771821 + 0.771821i 0.0246424 + 0.0246424i
\(982\) 38.2648 23.9140i 1.22108 0.763128i
\(983\) 45.7122i 1.45799i −0.684517 0.728997i \(-0.739987\pi\)
0.684517 0.728997i \(-0.260013\pi\)
\(984\) −26.5925 32.7070i −0.847738 1.04266i
\(985\) 36.9012i 1.17577i
\(986\) −1.32707 2.12345i −0.0422626 0.0676243i
\(987\) 3.14627 + 3.14627i 0.100147 + 0.100147i
\(988\) −5.68238 + 11.6545i −0.180781 + 0.370780i
\(989\) 52.3653 + 52.3653i 1.66512 + 1.66512i
\(990\) −6.09851 + 26.4235i −0.193823 + 0.839795i
\(991\) 43.7372i 1.38936i 0.719319 + 0.694679i \(0.244454\pi\)
−0.719319 + 0.694679i \(0.755546\pi\)
\(992\) 16.6120 + 35.5938i 0.527432 + 1.13011i
\(993\) −63.8617 −2.02659
\(994\) −9.79551 2.26079i −0.310695 0.0717078i
\(995\) 25.0885 25.0885i 0.795358 0.795358i
\(996\) −52.3429 25.5207i −1.65855 0.808656i
\(997\) −5.72412 5.72412i −0.181285 0.181285i 0.610631 0.791915i \(-0.290916\pi\)
−0.791915 + 0.610631i \(0.790916\pi\)
\(998\) 48.1775 30.1091i 1.52503 0.953086i
\(999\) 11.5605 0.365757
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 656.2.o.a.573.8 yes 164
16.5 even 4 inner 656.2.o.a.245.7 164
41.40 even 2 inner 656.2.o.a.573.7 yes 164
656.245 even 4 inner 656.2.o.a.245.8 yes 164
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
656.2.o.a.245.7 164 16.5 even 4 inner
656.2.o.a.245.8 yes 164 656.245 even 4 inner
656.2.o.a.573.7 yes 164 41.40 even 2 inner
656.2.o.a.573.8 yes 164 1.1 even 1 trivial