Properties

Label 525.2.j.c.218.8
Level $525$
Weight $2$
Character 525.218
Analytic conductor $4.192$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(218,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.218");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.8
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.c.407.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.723969 - 0.723969i) q^{2} +(1.41842 - 0.994020i) q^{3} -0.951738i q^{4} +(-1.74653 - 0.307254i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.13697 + 2.13697i) q^{8} +(1.02385 - 2.81988i) q^{9} +O(q^{10})\) \(q+(-0.723969 - 0.723969i) q^{2} +(1.41842 - 0.994020i) q^{3} -0.951738i q^{4} +(-1.74653 - 0.307254i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.13697 + 2.13697i) q^{8} +(1.02385 - 2.81988i) q^{9} -3.63664i q^{11} +(-0.946047 - 1.34997i) q^{12} +(4.19487 + 4.19487i) q^{13} -1.02385 q^{14} +1.19072 q^{16} +(-4.61300 - 4.61300i) q^{17} +(-2.78274 + 1.30027i) q^{18} -3.77162i q^{19} +(0.300098 - 1.70586i) q^{21} +(-2.63281 + 2.63281i) q^{22} +(-1.81887 + 1.81887i) q^{23} +(-0.906934 + 5.15531i) q^{24} -6.07391i q^{26} +(-1.35077 - 5.01751i) q^{27} +(-0.672980 - 0.672980i) q^{28} +1.13909 q^{29} +3.62492 q^{31} +(3.41189 + 3.41189i) q^{32} +(-3.61489 - 5.15829i) q^{33} +6.67933i q^{34} +(-2.68379 - 0.974434i) q^{36} +(-7.24824 + 7.24824i) q^{37} +(-2.73054 + 2.73054i) q^{38} +(10.1199 + 1.78031i) q^{39} +0.314852i q^{41} +(-1.45225 + 1.01772i) q^{42} +(1.06556 + 1.06556i) q^{43} -3.46112 q^{44} +2.63362 q^{46} +(4.48582 + 4.48582i) q^{47} +(1.68894 - 1.18360i) q^{48} -1.00000i q^{49} +(-11.1286 - 1.95777i) q^{51} +(3.99242 - 3.99242i) q^{52} +(1.44794 - 1.44794i) q^{53} +(-2.65460 + 4.61044i) q^{54} +3.02213i q^{56} +(-3.74907 - 5.34975i) q^{57} +(-0.824666 - 0.824666i) q^{58} -8.70646 q^{59} +3.08903 q^{61} +(-2.62433 - 2.62433i) q^{62} +(-1.26999 - 2.71793i) q^{63} -7.32164i q^{64} +(-1.11737 + 6.35151i) q^{66} +(9.67044 - 9.67044i) q^{67} +(-4.39036 + 4.39036i) q^{68} +(-0.771934 + 4.38793i) q^{69} +10.4601i q^{71} +(3.83807 + 8.21392i) q^{72} +(-0.710104 - 0.710104i) q^{73} +10.4950 q^{74} -3.58959 q^{76} +(-2.57149 - 2.57149i) q^{77} +(-6.03759 - 8.61538i) q^{78} -7.30426i q^{79} +(-6.90348 - 5.77426i) q^{81} +(0.227943 - 0.227943i) q^{82} +(9.58225 - 9.58225i) q^{83} +(-1.62353 - 0.285614i) q^{84} -1.54287i q^{86} +(1.61571 - 1.13228i) q^{87} +(7.77137 + 7.77137i) q^{88} +15.5299 q^{89} +5.93244 q^{91} +(1.73109 + 1.73109i) q^{92} +(5.14167 - 3.60325i) q^{93} -6.49519i q^{94} +(8.23099 + 1.44801i) q^{96} +(-5.28841 + 5.28841i) q^{97} +(-0.723969 + 0.723969i) q^{98} +(-10.2549 - 3.72336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.723969 0.723969i −0.511923 0.511923i 0.403192 0.915115i \(-0.367901\pi\)
−0.915115 + 0.403192i \(0.867901\pi\)
\(3\) 1.41842 0.994020i 0.818927 0.573898i
\(4\) 0.951738i 0.475869i
\(5\) 0 0
\(6\) −1.74653 0.307254i −0.713020 0.125436i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) −2.13697 + 2.13697i −0.755532 + 0.755532i
\(9\) 1.02385 2.81988i 0.341282 0.939961i
\(10\) 0 0
\(11\) 3.63664i 1.09649i −0.836319 0.548243i \(-0.815297\pi\)
0.836319 0.548243i \(-0.184703\pi\)
\(12\) −0.946047 1.34997i −0.273100 0.389702i
\(13\) 4.19487 + 4.19487i 1.16345 + 1.16345i 0.983716 + 0.179732i \(0.0575231\pi\)
0.179732 + 0.983716i \(0.442477\pi\)
\(14\) −1.02385 −0.273635
\(15\) 0 0
\(16\) 1.19072 0.297680
\(17\) −4.61300 4.61300i −1.11882 1.11882i −0.991915 0.126901i \(-0.959497\pi\)
−0.126901 0.991915i \(-0.540503\pi\)
\(18\) −2.78274 + 1.30027i −0.655898 + 0.306478i
\(19\) 3.77162i 0.865269i −0.901569 0.432635i \(-0.857584\pi\)
0.901569 0.432635i \(-0.142416\pi\)
\(20\) 0 0
\(21\) 0.300098 1.70586i 0.0654867 0.372248i
\(22\) −2.63281 + 2.63281i −0.561317 + 0.561317i
\(23\) −1.81887 + 1.81887i −0.379261 + 0.379261i −0.870836 0.491574i \(-0.836422\pi\)
0.491574 + 0.870836i \(0.336422\pi\)
\(24\) −0.906934 + 5.15531i −0.185127 + 1.05232i
\(25\) 0 0
\(26\) 6.07391i 1.19119i
\(27\) −1.35077 5.01751i −0.259956 0.965620i
\(28\) −0.672980 0.672980i −0.127181 0.127181i
\(29\) 1.13909 0.211524 0.105762 0.994391i \(-0.466272\pi\)
0.105762 + 0.994391i \(0.466272\pi\)
\(30\) 0 0
\(31\) 3.62492 0.651055 0.325528 0.945532i \(-0.394458\pi\)
0.325528 + 0.945532i \(0.394458\pi\)
\(32\) 3.41189 + 3.41189i 0.603142 + 0.603142i
\(33\) −3.61489 5.15829i −0.629272 0.897943i
\(34\) 6.67933i 1.14550i
\(35\) 0 0
\(36\) −2.68379 0.974434i −0.447298 0.162406i
\(37\) −7.24824 + 7.24824i −1.19160 + 1.19160i −0.214987 + 0.976617i \(0.568971\pi\)
−0.976617 + 0.214987i \(0.931029\pi\)
\(38\) −2.73054 + 2.73054i −0.442951 + 0.442951i
\(39\) 10.1199 + 1.78031i 1.62048 + 0.285078i
\(40\) 0 0
\(41\) 0.314852i 0.0491716i 0.999698 + 0.0245858i \(0.00782669\pi\)
−0.999698 + 0.0245858i \(0.992173\pi\)
\(42\) −1.45225 + 1.01772i −0.224087 + 0.157038i
\(43\) 1.06556 + 1.06556i 0.162497 + 0.162497i 0.783672 0.621175i \(-0.213344\pi\)
−0.621175 + 0.783672i \(0.713344\pi\)
\(44\) −3.46112 −0.521784
\(45\) 0 0
\(46\) 2.63362 0.388306
\(47\) 4.48582 + 4.48582i 0.654324 + 0.654324i 0.954031 0.299707i \(-0.0968889\pi\)
−0.299707 + 0.954031i \(0.596889\pi\)
\(48\) 1.68894 1.18360i 0.243778 0.170838i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −11.1286 1.95777i −1.55831 0.274142i
\(52\) 3.99242 3.99242i 0.553648 0.553648i
\(53\) 1.44794 1.44794i 0.198890 0.198890i −0.600634 0.799524i \(-0.705085\pi\)
0.799524 + 0.600634i \(0.205085\pi\)
\(54\) −2.65460 + 4.61044i −0.361246 + 0.627401i
\(55\) 0 0
\(56\) 3.02213i 0.403849i
\(57\) −3.74907 5.34975i −0.496576 0.708592i
\(58\) −0.824666 0.824666i −0.108284 0.108284i
\(59\) −8.70646 −1.13348 −0.566742 0.823895i \(-0.691796\pi\)
−0.566742 + 0.823895i \(0.691796\pi\)
\(60\) 0 0
\(61\) 3.08903 0.395509 0.197755 0.980252i \(-0.436635\pi\)
0.197755 + 0.980252i \(0.436635\pi\)
\(62\) −2.62433 2.62433i −0.333291 0.333291i
\(63\) −1.26999 2.71793i −0.160004 0.342427i
\(64\) 7.32164i 0.915205i
\(65\) 0 0
\(66\) −1.11737 + 6.35151i −0.137539 + 0.781817i
\(67\) 9.67044 9.67044i 1.18143 1.18143i 0.202060 0.979373i \(-0.435237\pi\)
0.979373 0.202060i \(-0.0647635\pi\)
\(68\) −4.39036 + 4.39036i −0.532410 + 0.532410i
\(69\) −0.771934 + 4.38793i −0.0929300 + 0.528245i
\(70\) 0 0
\(71\) 10.4601i 1.24138i 0.784056 + 0.620690i \(0.213147\pi\)
−0.784056 + 0.620690i \(0.786853\pi\)
\(72\) 3.83807 + 8.21392i 0.452321 + 0.968020i
\(73\) −0.710104 0.710104i −0.0831114 0.0831114i 0.664329 0.747440i \(-0.268717\pi\)
−0.747440 + 0.664329i \(0.768717\pi\)
\(74\) 10.4950 1.22002
\(75\) 0 0
\(76\) −3.58959 −0.411755
\(77\) −2.57149 2.57149i −0.293048 0.293048i
\(78\) −6.03759 8.61538i −0.683623 0.975499i
\(79\) 7.30426i 0.821793i −0.911682 0.410897i \(-0.865216\pi\)
0.911682 0.410897i \(-0.134784\pi\)
\(80\) 0 0
\(81\) −6.90348 5.77426i −0.767053 0.641584i
\(82\) 0.227943 0.227943i 0.0251721 0.0251721i
\(83\) 9.58225 9.58225i 1.05179 1.05179i 0.0532053 0.998584i \(-0.483056\pi\)
0.998584 0.0532053i \(-0.0169438\pi\)
\(84\) −1.62353 0.285614i −0.177141 0.0311631i
\(85\) 0 0
\(86\) 1.54287i 0.166372i
\(87\) 1.61571 1.13228i 0.173223 0.121393i
\(88\) 7.77137 + 7.77137i 0.828431 + 0.828431i
\(89\) 15.5299 1.64616 0.823082 0.567923i \(-0.192253\pi\)
0.823082 + 0.567923i \(0.192253\pi\)
\(90\) 0 0
\(91\) 5.93244 0.621889
\(92\) 1.73109 + 1.73109i 0.180479 + 0.180479i
\(93\) 5.14167 3.60325i 0.533167 0.373639i
\(94\) 6.49519i 0.669928i
\(95\) 0 0
\(96\) 8.23099 + 1.44801i 0.840072 + 0.147787i
\(97\) −5.28841 + 5.28841i −0.536957 + 0.536957i −0.922634 0.385677i \(-0.873968\pi\)
0.385677 + 0.922634i \(0.373968\pi\)
\(98\) −0.723969 + 0.723969i −0.0731319 + 0.0731319i
\(99\) −10.2549 3.72336i −1.03065 0.374212i
\(100\) 0 0
\(101\) 5.52857i 0.550114i 0.961428 + 0.275057i \(0.0886966\pi\)
−0.961428 + 0.275057i \(0.911303\pi\)
\(102\) 6.63939 + 9.47412i 0.657398 + 0.938078i
\(103\) 1.67893 + 1.67893i 0.165430 + 0.165430i 0.784967 0.619538i \(-0.212680\pi\)
−0.619538 + 0.784967i \(0.712680\pi\)
\(104\) −17.9286 −1.75804
\(105\) 0 0
\(106\) −2.09652 −0.203632
\(107\) 6.33012 + 6.33012i 0.611956 + 0.611956i 0.943455 0.331500i \(-0.107555\pi\)
−0.331500 + 0.943455i \(0.607555\pi\)
\(108\) −4.77535 + 1.28558i −0.459509 + 0.123705i
\(109\) 6.19191i 0.593078i 0.955021 + 0.296539i \(0.0958324\pi\)
−0.955021 + 0.296539i \(0.904168\pi\)
\(110\) 0 0
\(111\) −3.07617 + 17.4860i −0.291977 + 1.65970i
\(112\) 0.841966 0.841966i 0.0795583 0.0795583i
\(113\) 1.87617 1.87617i 0.176495 0.176495i −0.613331 0.789826i \(-0.710171\pi\)
0.789826 + 0.613331i \(0.210171\pi\)
\(114\) −1.15885 + 6.58726i −0.108536 + 0.616954i
\(115\) 0 0
\(116\) 1.08412i 0.100658i
\(117\) 16.1239 7.53414i 1.49066 0.696531i
\(118\) 6.30320 + 6.30320i 0.580257 + 0.580257i
\(119\) −6.52376 −0.598032
\(120\) 0 0
\(121\) −2.22512 −0.202284
\(122\) −2.23636 2.23636i −0.202470 0.202470i
\(123\) 0.312969 + 0.446593i 0.0282195 + 0.0402680i
\(124\) 3.44998i 0.309817i
\(125\) 0 0
\(126\) −1.04826 + 2.88713i −0.0933866 + 0.257206i
\(127\) −3.43180 + 3.43180i −0.304523 + 0.304523i −0.842781 0.538257i \(-0.819083\pi\)
0.538257 + 0.842781i \(0.319083\pi\)
\(128\) 1.52313 1.52313i 0.134627 0.134627i
\(129\) 2.57061 + 0.452227i 0.226329 + 0.0398164i
\(130\) 0 0
\(131\) 3.84637i 0.336059i 0.985782 + 0.168029i \(0.0537403\pi\)
−0.985782 + 0.168029i \(0.946260\pi\)
\(132\) −4.90934 + 3.44043i −0.427303 + 0.299451i
\(133\) −2.66694 2.66694i −0.231253 0.231253i
\(134\) −14.0022 −1.20961
\(135\) 0 0
\(136\) 19.7156 1.69060
\(137\) 13.6056 + 13.6056i 1.16241 + 1.16241i 0.983947 + 0.178459i \(0.0571111\pi\)
0.178459 + 0.983947i \(0.442889\pi\)
\(138\) 3.73558 2.61787i 0.317994 0.222848i
\(139\) 9.05369i 0.767924i −0.923349 0.383962i \(-0.874559\pi\)
0.923349 0.383962i \(-0.125441\pi\)
\(140\) 0 0
\(141\) 10.8218 + 1.90379i 0.911359 + 0.160328i
\(142\) 7.57276 7.57276i 0.635492 0.635492i
\(143\) 15.2552 15.2552i 1.27571 1.27571i
\(144\) 1.21911 3.35769i 0.101593 0.279808i
\(145\) 0 0
\(146\) 1.02819i 0.0850934i
\(147\) −0.994020 1.41842i −0.0819854 0.116990i
\(148\) 6.89843 + 6.89843i 0.567047 + 0.567047i
\(149\) 20.5997 1.68759 0.843796 0.536663i \(-0.180315\pi\)
0.843796 + 0.536663i \(0.180315\pi\)
\(150\) 0 0
\(151\) 15.9282 1.29622 0.648109 0.761547i \(-0.275560\pi\)
0.648109 + 0.761547i \(0.275560\pi\)
\(152\) 8.05983 + 8.05983i 0.653738 + 0.653738i
\(153\) −17.7311 + 8.28511i −1.43348 + 0.669811i
\(154\) 3.72336i 0.300037i
\(155\) 0 0
\(156\) 1.69439 9.63148i 0.135660 0.771135i
\(157\) −4.00609 + 4.00609i −0.319721 + 0.319721i −0.848660 0.528939i \(-0.822590\pi\)
0.528939 + 0.848660i \(0.322590\pi\)
\(158\) −5.28806 + 5.28806i −0.420695 + 0.420695i
\(159\) 0.614508 3.49307i 0.0487337 0.277018i
\(160\) 0 0
\(161\) 2.57228i 0.202724i
\(162\) 0.817520 + 9.17828i 0.0642304 + 0.721114i
\(163\) 5.18238 + 5.18238i 0.405915 + 0.405915i 0.880311 0.474396i \(-0.157334\pi\)
−0.474396 + 0.880311i \(0.657334\pi\)
\(164\) 0.299656 0.0233992
\(165\) 0 0
\(166\) −13.8745 −1.07687
\(167\) −7.76731 7.76731i −0.601053 0.601053i 0.339539 0.940592i \(-0.389729\pi\)
−0.940592 + 0.339539i \(0.889729\pi\)
\(168\) 3.00406 + 4.28665i 0.231768 + 0.330723i
\(169\) 22.1939i 1.70722i
\(170\) 0 0
\(171\) −10.6355 3.86156i −0.813319 0.295301i
\(172\) 1.01414 1.01414i 0.0773271 0.0773271i
\(173\) 0.953760 0.953760i 0.0725131 0.0725131i −0.669920 0.742433i \(-0.733672\pi\)
0.742433 + 0.669920i \(0.233672\pi\)
\(174\) −1.98946 0.349990i −0.150821 0.0265327i
\(175\) 0 0
\(176\) 4.33021i 0.326402i
\(177\) −12.3494 + 8.65440i −0.928241 + 0.650504i
\(178\) −11.2431 11.2431i −0.842710 0.842710i
\(179\) 19.1906 1.43437 0.717187 0.696881i \(-0.245429\pi\)
0.717187 + 0.696881i \(0.245429\pi\)
\(180\) 0 0
\(181\) 6.81119 0.506272 0.253136 0.967431i \(-0.418538\pi\)
0.253136 + 0.967431i \(0.418538\pi\)
\(182\) −4.29490 4.29490i −0.318359 0.318359i
\(183\) 4.38154 3.07055i 0.323893 0.226982i
\(184\) 7.77374i 0.573088i
\(185\) 0 0
\(186\) −6.33105 1.11377i −0.464215 0.0816658i
\(187\) −16.7758 + 16.7758i −1.22677 + 1.22677i
\(188\) 4.26933 4.26933i 0.311373 0.311373i
\(189\) −4.50306 2.59277i −0.327549 0.188597i
\(190\) 0 0
\(191\) 24.6052i 1.78037i 0.455602 + 0.890183i \(0.349424\pi\)
−0.455602 + 0.890183i \(0.650576\pi\)
\(192\) −7.27786 10.3852i −0.525235 0.749486i
\(193\) −16.1551 16.1551i −1.16287 1.16287i −0.983844 0.179026i \(-0.942705\pi\)
−0.179026 0.983844i \(-0.557295\pi\)
\(194\) 7.65729 0.549762
\(195\) 0 0
\(196\) −0.951738 −0.0679813
\(197\) −17.2478 17.2478i −1.22886 1.22886i −0.964397 0.264459i \(-0.914807\pi\)
−0.264459 0.964397i \(-0.585193\pi\)
\(198\) 4.72862 + 10.1198i 0.336049 + 0.719184i
\(199\) 17.1682i 1.21702i 0.793547 + 0.608509i \(0.208232\pi\)
−0.793547 + 0.608509i \(0.791768\pi\)
\(200\) 0 0
\(201\) 4.10416 23.3294i 0.289485 1.64553i
\(202\) 4.00252 4.00252i 0.281616 0.281616i
\(203\) 0.805459 0.805459i 0.0565321 0.0565321i
\(204\) −1.86328 + 10.5915i −0.130456 + 0.741554i
\(205\) 0 0
\(206\) 2.43098i 0.169374i
\(207\) 3.26676 + 6.99126i 0.227056 + 0.485926i
\(208\) 4.99492 + 4.99492i 0.346335 + 0.346335i
\(209\) −13.7160 −0.948756
\(210\) 0 0
\(211\) −12.4888 −0.859766 −0.429883 0.902884i \(-0.641445\pi\)
−0.429883 + 0.902884i \(0.641445\pi\)
\(212\) −1.37806 1.37806i −0.0946454 0.0946454i
\(213\) 10.3975 + 14.8368i 0.712426 + 1.01660i
\(214\) 9.16562i 0.626549i
\(215\) 0 0
\(216\) 13.6088 + 7.83570i 0.925962 + 0.533152i
\(217\) 2.56321 2.56321i 0.174002 0.174002i
\(218\) 4.48275 4.48275i 0.303610 0.303610i
\(219\) −1.71309 0.301370i −0.115760 0.0203647i
\(220\) 0 0
\(221\) 38.7018i 2.60337i
\(222\) 14.8864 10.4323i 0.999107 0.700167i
\(223\) −14.6702 14.6702i −0.982386 0.982386i 0.0174612 0.999848i \(-0.494442\pi\)
−0.999848 + 0.0174612i \(0.994442\pi\)
\(224\) 4.82514 0.322393
\(225\) 0 0
\(226\) −2.71657 −0.180704
\(227\) 1.58995 + 1.58995i 0.105528 + 0.105528i 0.757900 0.652371i \(-0.226226\pi\)
−0.652371 + 0.757900i \(0.726226\pi\)
\(228\) −5.09156 + 3.56813i −0.337197 + 0.236305i
\(229\) 1.35671i 0.0896541i 0.998995 + 0.0448270i \(0.0142737\pi\)
−0.998995 + 0.0448270i \(0.985726\pi\)
\(230\) 0 0
\(231\) −6.20357 1.09135i −0.408165 0.0718053i
\(232\) −2.43420 + 2.43420i −0.159813 + 0.159813i
\(233\) −15.1279 + 15.1279i −0.991061 + 0.991061i −0.999960 0.00889977i \(-0.997167\pi\)
0.00889977 + 0.999960i \(0.497167\pi\)
\(234\) −17.1277 6.21876i −1.11967 0.406533i
\(235\) 0 0
\(236\) 8.28626i 0.539390i
\(237\) −7.26058 10.3605i −0.471625 0.672989i
\(238\) 4.72300 + 4.72300i 0.306147 + 0.306147i
\(239\) 12.4988 0.808483 0.404242 0.914652i \(-0.367535\pi\)
0.404242 + 0.914652i \(0.367535\pi\)
\(240\) 0 0
\(241\) −18.0373 −1.16188 −0.580942 0.813945i \(-0.697316\pi\)
−0.580942 + 0.813945i \(0.697316\pi\)
\(242\) 1.61092 + 1.61092i 0.103554 + 0.103554i
\(243\) −15.5318 1.32814i −0.996364 0.0852003i
\(244\) 2.93994i 0.188210i
\(245\) 0 0
\(246\) 0.0967396 0.549900i 0.00616789 0.0350603i
\(247\) 15.8215 15.8215i 1.00670 1.00670i
\(248\) −7.74634 + 7.74634i −0.491893 + 0.491893i
\(249\) 4.06673 23.1166i 0.257719 1.46496i
\(250\) 0 0
\(251\) 5.34538i 0.337398i −0.985668 0.168699i \(-0.946043\pi\)
0.985668 0.168699i \(-0.0539565\pi\)
\(252\) −2.58675 + 1.20870i −0.162950 + 0.0761407i
\(253\) 6.61458 + 6.61458i 0.415855 + 0.415855i
\(254\) 4.96904 0.311785
\(255\) 0 0
\(256\) −16.8487 −1.05304
\(257\) −11.6091 11.6091i −0.724155 0.724155i 0.245294 0.969449i \(-0.421115\pi\)
−0.969449 + 0.245294i \(0.921115\pi\)
\(258\) −1.53364 2.18844i −0.0954803 0.136246i
\(259\) 10.2506i 0.636939i
\(260\) 0 0
\(261\) 1.16625 3.21210i 0.0721893 0.198824i
\(262\) 2.78465 2.78465i 0.172036 0.172036i
\(263\) 3.90300 3.90300i 0.240669 0.240669i −0.576458 0.817127i \(-0.695565\pi\)
0.817127 + 0.576458i \(0.195565\pi\)
\(264\) 18.7480 + 3.29819i 1.15386 + 0.202989i
\(265\) 0 0
\(266\) 3.86156i 0.236768i
\(267\) 22.0279 15.4370i 1.34809 0.944730i
\(268\) −9.20373 9.20373i −0.562207 0.562207i
\(269\) −31.1948 −1.90198 −0.950989 0.309225i \(-0.899930\pi\)
−0.950989 + 0.309225i \(0.899930\pi\)
\(270\) 0 0
\(271\) −19.4757 −1.18306 −0.591532 0.806282i \(-0.701477\pi\)
−0.591532 + 0.806282i \(0.701477\pi\)
\(272\) −5.49279 5.49279i −0.333049 0.333049i
\(273\) 8.41471 5.89697i 0.509282 0.356901i
\(274\) 19.7001i 1.19013i
\(275\) 0 0
\(276\) 4.17616 + 0.734679i 0.251375 + 0.0442225i
\(277\) −1.91736 + 1.91736i −0.115203 + 0.115203i −0.762358 0.647155i \(-0.775959\pi\)
0.647155 + 0.762358i \(0.275959\pi\)
\(278\) −6.55459 + 6.55459i −0.393118 + 0.393118i
\(279\) 3.71137 10.2219i 0.222194 0.611967i
\(280\) 0 0
\(281\) 0.320414i 0.0191143i −0.999954 0.00955715i \(-0.996958\pi\)
0.999954 0.00955715i \(-0.00304218\pi\)
\(282\) −6.45635 9.21293i −0.384470 0.548622i
\(283\) −1.20675 1.20675i −0.0717340 0.0717340i 0.670330 0.742064i \(-0.266153\pi\)
−0.742064 + 0.670330i \(0.766153\pi\)
\(284\) 9.95523 0.590734
\(285\) 0 0
\(286\) −22.0886 −1.30613
\(287\) 0.222634 + 0.222634i 0.0131417 + 0.0131417i
\(288\) 13.1144 6.12787i 0.772772 0.361088i
\(289\) 25.5595i 1.50350i
\(290\) 0 0
\(291\) −2.24441 + 12.7580i −0.131570 + 0.747887i
\(292\) −0.675833 + 0.675833i −0.0395501 + 0.0395501i
\(293\) −11.2016 + 11.2016i −0.654402 + 0.654402i −0.954050 0.299648i \(-0.903131\pi\)
0.299648 + 0.954050i \(0.403131\pi\)
\(294\) −0.307254 + 1.74653i −0.0179194 + 0.101860i
\(295\) 0 0
\(296\) 30.9785i 1.80059i
\(297\) −18.2469 + 4.91227i −1.05879 + 0.285039i
\(298\) −14.9135 14.9135i −0.863918 0.863918i
\(299\) −15.2599 −0.882502
\(300\) 0 0
\(301\) 1.50693 0.0868581
\(302\) −11.5315 11.5315i −0.663565 0.663565i
\(303\) 5.49551 + 7.84185i 0.315709 + 0.450503i
\(304\) 4.49094i 0.257573i
\(305\) 0 0
\(306\) 18.8349 + 6.83862i 1.07672 + 0.390938i
\(307\) −16.0589 + 16.0589i −0.916529 + 0.916529i −0.996775 0.0802463i \(-0.974429\pi\)
0.0802463 + 0.996775i \(0.474429\pi\)
\(308\) −2.44738 + 2.44738i −0.139453 + 0.139453i
\(309\) 4.05031 + 0.712540i 0.230414 + 0.0405350i
\(310\) 0 0
\(311\) 0.709997i 0.0402602i 0.999797 + 0.0201301i \(0.00640805\pi\)
−0.999797 + 0.0201301i \(0.993592\pi\)
\(312\) −25.4303 + 17.8214i −1.43971 + 1.00894i
\(313\) 14.9431 + 14.9431i 0.844632 + 0.844632i 0.989457 0.144826i \(-0.0462621\pi\)
−0.144826 + 0.989457i \(0.546262\pi\)
\(314\) 5.80057 0.327345
\(315\) 0 0
\(316\) −6.95174 −0.391066
\(317\) −3.83925 3.83925i −0.215634 0.215634i 0.591022 0.806656i \(-0.298725\pi\)
−0.806656 + 0.591022i \(0.798725\pi\)
\(318\) −2.97376 + 2.08399i −0.166760 + 0.116864i
\(319\) 4.14246i 0.231933i
\(320\) 0 0
\(321\) 15.2711 + 2.68652i 0.852347 + 0.149947i
\(322\) 1.86225 1.86225i 0.103779 0.103779i
\(323\) −17.3985 + 17.3985i −0.968077 + 0.968077i
\(324\) −5.49558 + 6.57030i −0.305310 + 0.365017i
\(325\) 0 0
\(326\) 7.50376i 0.415595i
\(327\) 6.15489 + 8.78275i 0.340366 + 0.485687i
\(328\) −0.672828 0.672828i −0.0371507 0.0371507i
\(329\) 6.34391 0.349751
\(330\) 0 0
\(331\) 31.8078 1.74831 0.874157 0.485644i \(-0.161415\pi\)
0.874157 + 0.485644i \(0.161415\pi\)
\(332\) −9.11979 9.11979i −0.500514 0.500514i
\(333\) 13.0181 + 27.8603i 0.713388 + 1.52673i
\(334\) 11.2466i 0.615386i
\(335\) 0 0
\(336\) 0.357333 2.03120i 0.0194941 0.110811i
\(337\) 12.8338 12.8338i 0.699104 0.699104i −0.265113 0.964217i \(-0.585409\pi\)
0.964217 + 0.265113i \(0.0854093\pi\)
\(338\) 16.0677 16.0677i 0.873966 0.873966i
\(339\) 0.796250 4.52615i 0.0432464 0.245827i
\(340\) 0 0
\(341\) 13.1825i 0.713874i
\(342\) 4.90414 + 10.4954i 0.265186 + 0.567529i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −4.55414 −0.245543
\(345\) 0 0
\(346\) −1.38099 −0.0742423
\(347\) 17.4728 + 17.4728i 0.937989 + 0.937989i 0.998187 0.0601971i \(-0.0191729\pi\)
−0.0601971 + 0.998187i \(0.519173\pi\)
\(348\) −1.07763 1.53773i −0.0577672 0.0824312i
\(349\) 2.27784i 0.121930i 0.998140 + 0.0609649i \(0.0194178\pi\)
−0.998140 + 0.0609649i \(0.980582\pi\)
\(350\) 0 0
\(351\) 15.3815 26.7141i 0.821003 1.42589i
\(352\) 12.4078 12.4078i 0.661338 0.661338i
\(353\) −0.992444 + 0.992444i −0.0528225 + 0.0528225i −0.733025 0.680202i \(-0.761892\pi\)
0.680202 + 0.733025i \(0.261892\pi\)
\(354\) 15.2061 + 2.67510i 0.808196 + 0.142180i
\(355\) 0 0
\(356\) 14.7804i 0.783358i
\(357\) −9.25346 + 6.48475i −0.489745 + 0.343210i
\(358\) −13.8934 13.8934i −0.734289 0.734289i
\(359\) −4.68580 −0.247307 −0.123654 0.992325i \(-0.539461\pi\)
−0.123654 + 0.992325i \(0.539461\pi\)
\(360\) 0 0
\(361\) 4.77488 0.251310
\(362\) −4.93109 4.93109i −0.259172 0.259172i
\(363\) −3.15616 + 2.21181i −0.165655 + 0.116090i
\(364\) 5.64613i 0.295938i
\(365\) 0 0
\(366\) −5.39509 0.949116i −0.282006 0.0496111i
\(367\) −8.68225 + 8.68225i −0.453210 + 0.453210i −0.896418 0.443209i \(-0.853840\pi\)
0.443209 + 0.896418i \(0.353840\pi\)
\(368\) −2.16577 + 2.16577i −0.112899 + 0.112899i
\(369\) 0.887846 + 0.322360i 0.0462194 + 0.0167814i
\(370\) 0 0
\(371\) 2.04769i 0.106311i
\(372\) −3.42935 4.89353i −0.177803 0.253717i
\(373\) −14.4089 14.4089i −0.746062 0.746062i 0.227675 0.973737i \(-0.426888\pi\)
−0.973737 + 0.227675i \(0.926888\pi\)
\(374\) 24.2903 1.25602
\(375\) 0 0
\(376\) −19.1721 −0.988726
\(377\) 4.77834 + 4.77834i 0.246097 + 0.246097i
\(378\) 1.38298 + 5.13716i 0.0711331 + 0.264227i
\(379\) 14.3572i 0.737482i 0.929532 + 0.368741i \(0.120211\pi\)
−0.929532 + 0.368741i \(0.879789\pi\)
\(380\) 0 0
\(381\) −1.45647 + 8.27903i −0.0746170 + 0.424148i
\(382\) 17.8134 17.8134i 0.911411 0.911411i
\(383\) 10.9175 10.9175i 0.557860 0.557860i −0.370838 0.928698i \(-0.620929\pi\)
0.928698 + 0.370838i \(0.120929\pi\)
\(384\) 0.646422 3.67448i 0.0329876 0.187512i
\(385\) 0 0
\(386\) 23.3916i 1.19060i
\(387\) 4.09573 1.91379i 0.208198 0.0972832i
\(388\) 5.03318 + 5.03318i 0.255521 + 0.255521i
\(389\) −14.3250 −0.726304 −0.363152 0.931730i \(-0.618299\pi\)
−0.363152 + 0.931730i \(0.618299\pi\)
\(390\) 0 0
\(391\) 16.7809 0.848648
\(392\) 2.13697 + 2.13697i 0.107933 + 0.107933i
\(393\) 3.82337 + 5.45577i 0.192863 + 0.275207i
\(394\) 24.9738i 1.25816i
\(395\) 0 0
\(396\) −3.54366 + 9.75996i −0.178076 + 0.490456i
\(397\) −21.0767 + 21.0767i −1.05781 + 1.05781i −0.0595859 + 0.998223i \(0.518978\pi\)
−0.998223 + 0.0595859i \(0.981022\pi\)
\(398\) 12.4292 12.4292i 0.623020 0.623020i
\(399\) −6.43384 1.13186i −0.322095 0.0566636i
\(400\) 0 0
\(401\) 10.9494i 0.546788i 0.961902 + 0.273394i \(0.0881463\pi\)
−0.961902 + 0.273394i \(0.911854\pi\)
\(402\) −19.8610 + 13.9185i −0.990579 + 0.694191i
\(403\) 15.2061 + 15.2061i 0.757469 + 0.757469i
\(404\) 5.26175 0.261782
\(405\) 0 0
\(406\) −1.16625 −0.0578802
\(407\) 26.3592 + 26.3592i 1.30658 + 1.30658i
\(408\) 27.9651 19.5978i 1.38448 0.970233i
\(409\) 19.4500i 0.961739i −0.876792 0.480870i \(-0.840321\pi\)
0.876792 0.480870i \(-0.159679\pi\)
\(410\) 0 0
\(411\) 32.8228 + 5.77426i 1.61903 + 0.284823i
\(412\) 1.59790 1.59790i 0.0787227 0.0787227i
\(413\) −6.15639 + 6.15639i −0.302936 + 0.302936i
\(414\) 2.69642 7.42649i 0.132522 0.364992i
\(415\) 0 0
\(416\) 28.6249i 1.40345i
\(417\) −8.99956 12.8420i −0.440710 0.628874i
\(418\) 9.92997 + 9.92997i 0.485690 + 0.485690i
\(419\) −25.9297 −1.26675 −0.633373 0.773846i \(-0.718330\pi\)
−0.633373 + 0.773846i \(0.718330\pi\)
\(420\) 0 0
\(421\) −5.79961 −0.282656 −0.141328 0.989963i \(-0.545137\pi\)
−0.141328 + 0.989963i \(0.545137\pi\)
\(422\) 9.04153 + 9.04153i 0.440135 + 0.440135i
\(423\) 17.2423 8.05670i 0.838349 0.391730i
\(424\) 6.18839i 0.300535i
\(425\) 0 0
\(426\) 3.21390 18.2688i 0.155714 0.885128i
\(427\) 2.18427 2.18427i 0.105704 0.105704i
\(428\) 6.02461 6.02461i 0.291211 0.291211i
\(429\) 6.47435 36.8023i 0.312585 1.77683i
\(430\) 0 0
\(431\) 14.8759i 0.716545i 0.933617 + 0.358272i \(0.116634\pi\)
−0.933617 + 0.358272i \(0.883366\pi\)
\(432\) −1.60839 5.97445i −0.0773838 0.287446i
\(433\) −18.5862 18.5862i −0.893198 0.893198i 0.101625 0.994823i \(-0.467596\pi\)
−0.994823 + 0.101625i \(0.967596\pi\)
\(434\) −3.71137 −0.178151
\(435\) 0 0
\(436\) 5.89308 0.282227
\(437\) 6.86010 + 6.86010i 0.328163 + 0.328163i
\(438\) 1.02204 + 1.45840i 0.0488349 + 0.0696852i
\(439\) 15.6687i 0.747828i −0.927463 0.373914i \(-0.878016\pi\)
0.927463 0.373914i \(-0.121984\pi\)
\(440\) 0 0
\(441\) −2.81988 1.02385i −0.134280 0.0487546i
\(442\) −28.0189 + 28.0189i −1.33273 + 1.33273i
\(443\) −17.4278 + 17.4278i −0.828021 + 0.828021i −0.987243 0.159222i \(-0.949102\pi\)
0.159222 + 0.987243i \(0.449102\pi\)
\(444\) 16.6421 + 2.92771i 0.789797 + 0.138943i
\(445\) 0 0
\(446\) 21.2415i 1.00581i
\(447\) 29.2191 20.4765i 1.38202 0.968506i
\(448\) −5.17718 5.17718i −0.244599 0.244599i
\(449\) −0.620804 −0.0292975 −0.0146488 0.999893i \(-0.504663\pi\)
−0.0146488 + 0.999893i \(0.504663\pi\)
\(450\) 0 0
\(451\) 1.14500 0.0539160
\(452\) −1.78562 1.78562i −0.0839885 0.0839885i
\(453\) 22.5929 15.8330i 1.06151 0.743897i
\(454\) 2.30214i 0.108045i
\(455\) 0 0
\(456\) 19.4439 + 3.42061i 0.910543 + 0.160185i
\(457\) 9.10965 9.10965i 0.426131 0.426131i −0.461177 0.887308i \(-0.652573\pi\)
0.887308 + 0.461177i \(0.152573\pi\)
\(458\) 0.982218 0.982218i 0.0458960 0.0458960i
\(459\) −16.9147 + 29.3769i −0.789508 + 1.37120i
\(460\) 0 0
\(461\) 2.78274i 0.129605i 0.997898 + 0.0648025i \(0.0206418\pi\)
−0.997898 + 0.0648025i \(0.979358\pi\)
\(462\) 3.70109 + 5.28130i 0.172190 + 0.245708i
\(463\) 10.4466 + 10.4466i 0.485495 + 0.485495i 0.906881 0.421386i \(-0.138456\pi\)
−0.421386 + 0.906881i \(0.638456\pi\)
\(464\) 1.35634 0.0629664
\(465\) 0 0
\(466\) 21.9042 1.01469
\(467\) 15.9720 + 15.9720i 0.739097 + 0.739097i 0.972403 0.233306i \(-0.0749544\pi\)
−0.233306 + 0.972403i \(0.574954\pi\)
\(468\) −7.17052 15.3458i −0.331457 0.709358i
\(469\) 13.6761i 0.631502i
\(470\) 0 0
\(471\) −1.70020 + 9.66447i −0.0783409 + 0.445315i
\(472\) 18.6054 18.6054i 0.856383 0.856383i
\(473\) 3.87506 3.87506i 0.178175 0.178175i
\(474\) −2.24426 + 12.7571i −0.103082 + 0.585955i
\(475\) 0 0
\(476\) 6.20891i 0.284585i
\(477\) −2.60055 5.56548i −0.119071 0.254826i
\(478\) −9.04878 9.04878i −0.413882 0.413882i
\(479\) 10.8945 0.497782 0.248891 0.968531i \(-0.419934\pi\)
0.248891 + 0.968531i \(0.419934\pi\)
\(480\) 0 0
\(481\) −60.8109 −2.77274
\(482\) 13.0584 + 13.0584i 0.594796 + 0.594796i
\(483\) 2.55689 + 3.64857i 0.116343 + 0.166016i
\(484\) 2.11773i 0.0962604i
\(485\) 0 0
\(486\) 10.2830 + 12.2061i 0.466446 + 0.553678i
\(487\) 5.03387 5.03387i 0.228107 0.228107i −0.583795 0.811901i \(-0.698433\pi\)
0.811901 + 0.583795i \(0.198433\pi\)
\(488\) −6.60114 + 6.60114i −0.298820 + 0.298820i
\(489\) 12.5022 + 2.19941i 0.565368 + 0.0994609i
\(490\) 0 0
\(491\) 11.9196i 0.537922i 0.963151 + 0.268961i \(0.0866803\pi\)
−0.963151 + 0.268961i \(0.913320\pi\)
\(492\) 0.425040 0.297865i 0.0191623 0.0134288i
\(493\) −5.25462 5.25462i −0.236656 0.236656i
\(494\) −22.9085 −1.03070
\(495\) 0 0
\(496\) 4.31627 0.193806
\(497\) 7.39638 + 7.39638i 0.331773 + 0.331773i
\(498\) −19.6799 + 13.7915i −0.881878 + 0.618014i
\(499\) 0.966794i 0.0432797i −0.999766 0.0216398i \(-0.993111\pi\)
0.999766 0.0216398i \(-0.00688871\pi\)
\(500\) 0 0
\(501\) −18.7382 3.29647i −0.837161 0.147275i
\(502\) −3.86989 + 3.86989i −0.172722 + 0.172722i
\(503\) 3.21397 3.21397i 0.143304 0.143304i −0.631815 0.775119i \(-0.717690\pi\)
0.775119 + 0.631815i \(0.217690\pi\)
\(504\) 8.52204 + 3.09420i 0.379602 + 0.137826i
\(505\) 0 0
\(506\) 9.57750i 0.425772i
\(507\) 22.0612 + 31.4803i 0.979771 + 1.39809i
\(508\) 3.26618 + 3.26618i 0.144913 + 0.144913i
\(509\) −24.1223 −1.06920 −0.534601 0.845104i \(-0.679538\pi\)
−0.534601 + 0.845104i \(0.679538\pi\)
\(510\) 0 0
\(511\) −1.00424 −0.0444249
\(512\) 9.15166 + 9.15166i 0.404450 + 0.404450i
\(513\) −18.9241 + 5.09460i −0.835521 + 0.224932i
\(514\) 16.8092i 0.741423i
\(515\) 0 0
\(516\) 0.430401 2.44654i 0.0189474 0.107703i
\(517\) 16.3133 16.3133i 0.717458 0.717458i
\(518\) 7.42109 7.42109i 0.326064 0.326064i
\(519\) 0.404778 2.30089i 0.0177678 0.100998i
\(520\) 0 0
\(521\) 43.5258i 1.90690i −0.301554 0.953449i \(-0.597505\pi\)
0.301554 0.953449i \(-0.402495\pi\)
\(522\) −3.16979 + 1.48113i −0.138738 + 0.0648273i
\(523\) −7.55731 7.55731i −0.330458 0.330458i 0.522302 0.852760i \(-0.325073\pi\)
−0.852760 + 0.522302i \(0.825073\pi\)
\(524\) 3.66073 0.159920
\(525\) 0 0
\(526\) −5.65130 −0.246408
\(527\) −16.7218 16.7218i −0.728411 0.728411i
\(528\) −4.30432 6.14208i −0.187322 0.267300i
\(529\) 16.3834i 0.712322i
\(530\) 0 0
\(531\) −8.91408 + 24.5512i −0.386838 + 1.06543i
\(532\) −2.53823 + 2.53823i −0.110046 + 0.110046i
\(533\) −1.32076 + 1.32076i −0.0572086 + 0.0572086i
\(534\) −27.1235 4.77162i −1.17375 0.206488i
\(535\) 0 0
\(536\) 41.3308i 1.78522i
\(537\) 27.2204 19.0759i 1.17465 0.823184i
\(538\) 22.5840 + 22.5840i 0.973667 + 0.973667i
\(539\) −3.63664 −0.156641
\(540\) 0 0
\(541\) 21.5120 0.924873 0.462436 0.886652i \(-0.346975\pi\)
0.462436 + 0.886652i \(0.346975\pi\)
\(542\) 14.0998 + 14.0998i 0.605638 + 0.605638i
\(543\) 9.66115 6.77046i 0.414600 0.290548i
\(544\) 31.4781i 1.34961i
\(545\) 0 0
\(546\) −10.3612 1.82277i −0.443419 0.0780073i
\(547\) −4.12772 + 4.12772i −0.176489 + 0.176489i −0.789823 0.613335i \(-0.789828\pi\)
0.613335 + 0.789823i \(0.289828\pi\)
\(548\) 12.9490 12.9490i 0.553153 0.553153i
\(549\) 3.16269 8.71069i 0.134980 0.371763i
\(550\) 0 0
\(551\) 4.29622i 0.183025i
\(552\) −7.72726 11.0265i −0.328894 0.469317i
\(553\) −5.16489 5.16489i −0.219633 0.219633i
\(554\) 2.77622 0.117950
\(555\) 0 0
\(556\) −8.61674 −0.365431
\(557\) −30.3025 30.3025i −1.28396 1.28396i −0.938396 0.345560i \(-0.887689\pi\)
−0.345560 0.938396i \(-0.612311\pi\)
\(558\) −10.0872 + 4.71339i −0.427026 + 0.199534i
\(559\) 8.93978i 0.378113i
\(560\) 0 0
\(561\) −7.11969 + 40.4706i −0.300593 + 1.70867i
\(562\) −0.231970 + 0.231970i −0.00978505 + 0.00978505i
\(563\) −8.67504 + 8.67504i −0.365609 + 0.365609i −0.865873 0.500264i \(-0.833236\pi\)
0.500264 + 0.865873i \(0.333236\pi\)
\(564\) 1.81191 10.2995i 0.0762953 0.433687i
\(565\) 0 0
\(566\) 1.74730i 0.0734447i
\(567\) −8.96451 + 0.798479i −0.376474 + 0.0335330i
\(568\) −22.3528 22.3528i −0.937902 0.937902i
\(569\) −7.88148 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(570\) 0 0
\(571\) −11.5764 −0.484459 −0.242230 0.970219i \(-0.577879\pi\)
−0.242230 + 0.970219i \(0.577879\pi\)
\(572\) −14.5190 14.5190i −0.607068 0.607068i
\(573\) 24.4580 + 34.9005i 1.02175 + 1.45799i
\(574\) 0.322360i 0.0134551i
\(575\) 0 0
\(576\) −20.6462 7.49624i −0.860257 0.312343i
\(577\) 15.8784 15.8784i 0.661027 0.661027i −0.294595 0.955622i \(-0.595185\pi\)
0.955622 + 0.294595i \(0.0951849\pi\)
\(578\) 18.5043 18.5043i 0.769677 0.769677i
\(579\) −38.9733 6.85627i −1.61967 0.284937i
\(580\) 0 0
\(581\) 13.5514i 0.562205i
\(582\) 10.8613 7.61150i 0.450214 0.315507i
\(583\) −5.26562 5.26562i −0.218080 0.218080i
\(584\) 3.03494 0.125587
\(585\) 0 0
\(586\) 16.2192 0.670007
\(587\) 9.87937 + 9.87937i 0.407765 + 0.407765i 0.880959 0.473193i \(-0.156899\pi\)
−0.473193 + 0.880959i \(0.656899\pi\)
\(588\) −1.34997 + 0.946047i −0.0556717 + 0.0390143i
\(589\) 13.6718i 0.563338i
\(590\) 0 0
\(591\) −41.6094 7.32001i −1.71158 0.301105i
\(592\) −8.63063 + 8.63063i −0.354717 + 0.354717i
\(593\) 0.614696 0.614696i 0.0252426 0.0252426i −0.694373 0.719615i \(-0.744318\pi\)
0.719615 + 0.694373i \(0.244318\pi\)
\(594\) 16.7665 + 9.65383i 0.687937 + 0.396101i
\(595\) 0 0
\(596\) 19.6055i 0.803073i
\(597\) 17.0655 + 24.3517i 0.698445 + 0.996649i
\(598\) 11.0477 + 11.0477i 0.451773 + 0.451773i
\(599\) −15.3650 −0.627797 −0.313898 0.949457i \(-0.601635\pi\)
−0.313898 + 0.949457i \(0.601635\pi\)
\(600\) 0 0
\(601\) −26.6232 −1.08598 −0.542991 0.839738i \(-0.682708\pi\)
−0.542991 + 0.839738i \(0.682708\pi\)
\(602\) −1.09097 1.09097i −0.0444647 0.0444647i
\(603\) −17.3685 37.1706i −0.707299 1.51370i
\(604\) 15.1595i 0.616830i
\(605\) 0 0
\(606\) 1.69868 9.65584i 0.0690040 0.392242i
\(607\) −12.5800 + 12.5800i −0.510606 + 0.510606i −0.914712 0.404106i \(-0.867583\pi\)
0.404106 + 0.914712i \(0.367583\pi\)
\(608\) 12.8683 12.8683i 0.521880 0.521880i
\(609\) 0.341839 1.94312i 0.0138520 0.0787393i
\(610\) 0 0
\(611\) 37.6349i 1.52254i
\(612\) 7.88525 + 16.8754i 0.318742 + 0.682146i
\(613\) −26.4562 26.4562i −1.06856 1.06856i −0.997470 0.0710867i \(-0.977353\pi\)
−0.0710867 0.997470i \(-0.522647\pi\)
\(614\) 23.2523 0.938385
\(615\) 0 0
\(616\) 10.9904 0.442815
\(617\) −8.96074 8.96074i −0.360746 0.360746i 0.503342 0.864088i \(-0.332104\pi\)
−0.864088 + 0.503342i \(0.832104\pi\)
\(618\) −2.41644 3.44816i −0.0972037 0.138705i
\(619\) 23.8205i 0.957426i 0.877971 + 0.478713i \(0.158897\pi\)
−0.877971 + 0.478713i \(0.841103\pi\)
\(620\) 0 0
\(621\) 11.5831 + 6.66933i 0.464814 + 0.267631i
\(622\) 0.514016 0.514016i 0.0206101 0.0206101i
\(623\) 10.9813 10.9813i 0.439956 0.439956i
\(624\) 12.0500 + 2.11985i 0.482384 + 0.0848621i
\(625\) 0 0
\(626\) 21.6366i 0.864773i
\(627\) −19.4551 + 13.6340i −0.776962 + 0.544489i
\(628\) 3.81275 + 3.81275i 0.152145 + 0.152145i
\(629\) 66.8723 2.66637
\(630\) 0 0
\(631\) 20.2819 0.807410 0.403705 0.914889i \(-0.367722\pi\)
0.403705 + 0.914889i \(0.367722\pi\)
\(632\) 15.6090 + 15.6090i 0.620891 + 0.620891i
\(633\) −17.7144 + 12.4142i −0.704086 + 0.493418i
\(634\) 5.55900i 0.220776i
\(635\) 0 0
\(636\) −3.32448 0.584851i −0.131824 0.0231908i
\(637\) 4.19487 4.19487i 0.166207 0.166207i
\(638\) −2.99901 + 2.99901i −0.118732 + 0.118732i
\(639\) 29.4961 + 10.7095i 1.16685 + 0.423661i
\(640\) 0 0
\(641\) 27.5041i 1.08635i 0.839620 + 0.543174i \(0.182778\pi\)
−0.839620 + 0.543174i \(0.817222\pi\)
\(642\) −9.11081 13.0007i −0.359575 0.513098i
\(643\) 17.2643 + 17.2643i 0.680839 + 0.680839i 0.960189 0.279350i \(-0.0901190\pi\)
−0.279350 + 0.960189i \(0.590119\pi\)
\(644\) 2.44813 0.0964699
\(645\) 0 0
\(646\) 25.1919 0.991163
\(647\) 2.92523 + 2.92523i 0.115003 + 0.115003i 0.762266 0.647264i \(-0.224087\pi\)
−0.647264 + 0.762266i \(0.724087\pi\)
\(648\) 27.0919 2.41310i 1.06427 0.0947957i
\(649\) 31.6622i 1.24285i
\(650\) 0 0
\(651\) 1.08783 6.18359i 0.0426355 0.242354i
\(652\) 4.93226 4.93226i 0.193162 0.193162i
\(653\) −25.2123 + 25.2123i −0.986635 + 0.986635i −0.999912 0.0132769i \(-0.995774\pi\)
0.0132769 + 0.999912i \(0.495774\pi\)
\(654\) 1.90249 10.8144i 0.0743933 0.422876i
\(655\) 0 0
\(656\) 0.374901i 0.0146374i
\(657\) −2.72945 + 1.27537i −0.106486 + 0.0497570i
\(658\) −4.59280 4.59280i −0.179046 0.179046i
\(659\) 20.3603 0.793125 0.396563 0.918008i \(-0.370203\pi\)
0.396563 + 0.918008i \(0.370203\pi\)
\(660\) 0 0
\(661\) 17.8508 0.694314 0.347157 0.937807i \(-0.387147\pi\)
0.347157 + 0.937807i \(0.387147\pi\)
\(662\) −23.0278 23.0278i −0.895002 0.895002i
\(663\) −38.4704 54.8956i −1.49407 2.13197i
\(664\) 40.9539i 1.58932i
\(665\) 0 0
\(666\) 10.7453 29.5947i 0.416371 1.14677i
\(667\) −2.07186 + 2.07186i −0.0802228 + 0.0802228i
\(668\) −7.39244 + 7.39244i −0.286022 + 0.286022i
\(669\) −35.3909 6.22605i −1.36829 0.240713i
\(670\) 0 0
\(671\) 11.2337i 0.433671i
\(672\) 6.84409 4.79629i 0.264016 0.185021i
\(673\) 22.7637 + 22.7637i 0.877476 + 0.877476i 0.993273 0.115797i \(-0.0369421\pi\)
−0.115797 + 0.993273i \(0.536942\pi\)
\(674\) −18.5826 −0.715776
\(675\) 0 0
\(676\) 21.1227 0.812413
\(677\) 10.9347 + 10.9347i 0.420256 + 0.420256i 0.885292 0.465036i \(-0.153959\pi\)
−0.465036 + 0.885292i \(0.653959\pi\)
\(678\) −3.85325 + 2.70033i −0.147983 + 0.103706i
\(679\) 7.47894i 0.287015i
\(680\) 0 0
\(681\) 3.83566 + 0.674777i 0.146983 + 0.0258575i
\(682\) −9.54374 + 9.54374i −0.365449 + 0.365449i
\(683\) −6.50227 + 6.50227i −0.248802 + 0.248802i −0.820479 0.571677i \(-0.806293\pi\)
0.571677 + 0.820479i \(0.306293\pi\)
\(684\) −3.67519 + 10.1222i −0.140525 + 0.387033i
\(685\) 0 0
\(686\) 1.02385i 0.0390907i
\(687\) 1.34860 + 1.92439i 0.0514523 + 0.0734201i
\(688\) 1.26879 + 1.26879i 0.0483720 + 0.0483720i
\(689\) 12.1478 0.462795
\(690\) 0 0
\(691\) 27.4621 1.04471 0.522353 0.852729i \(-0.325054\pi\)
0.522353 + 0.852729i \(0.325054\pi\)
\(692\) −0.907730 0.907730i −0.0345067 0.0345067i
\(693\) −9.88411 + 4.61849i −0.375466 + 0.175442i
\(694\) 25.2995i 0.960357i
\(695\) 0 0
\(696\) −1.03308 + 5.87237i −0.0391588 + 0.222591i
\(697\) 1.45241 1.45241i 0.0550140 0.0550140i
\(698\) 1.64908 1.64908i 0.0624187 0.0624187i
\(699\) −6.42031 + 36.4952i −0.242838 + 1.38037i
\(700\) 0 0
\(701\) 22.1998i 0.838473i −0.907877 0.419237i \(-0.862298\pi\)
0.907877 0.419237i \(-0.137702\pi\)
\(702\) −30.4759 + 8.20448i −1.15024 + 0.309658i
\(703\) 27.3376 + 27.3376i 1.03106 + 1.03106i
\(704\) −26.6262 −1.00351
\(705\) 0 0
\(706\) 1.43700 0.0540821
\(707\) 3.90929 + 3.90929i 0.147024 + 0.147024i
\(708\) 8.23671 + 11.7534i 0.309555 + 0.441721i
\(709\) 29.2448i 1.09831i −0.835721 0.549155i \(-0.814950\pi\)
0.835721 0.549155i \(-0.185050\pi\)
\(710\) 0 0
\(711\) −20.5972 7.47844i −0.772453 0.280463i
\(712\) −33.1868 + 33.1868i −1.24373 + 1.24373i
\(713\) −6.59328 + 6.59328i −0.246920 + 0.246920i
\(714\) 11.3940 + 2.00445i 0.426409 + 0.0750148i
\(715\) 0 0
\(716\) 18.2644i 0.682574i
\(717\) 17.7287 12.4241i 0.662089 0.463987i
\(718\) 3.39237 + 3.39237i 0.126602 + 0.126602i
\(719\) −20.4862 −0.764006 −0.382003 0.924161i \(-0.624766\pi\)
−0.382003 + 0.924161i \(0.624766\pi\)
\(720\) 0 0
\(721\) 2.37436 0.0884258
\(722\) −3.45687 3.45687i −0.128651 0.128651i
\(723\) −25.5845 + 17.9294i −0.951498 + 0.666803i
\(724\) 6.48247i 0.240919i
\(725\) 0 0
\(726\) 3.88625 + 0.683677i 0.144232 + 0.0253736i
\(727\) −17.3682 + 17.3682i −0.644150 + 0.644150i −0.951573 0.307423i \(-0.900533\pi\)
0.307423 + 0.951573i \(0.400533\pi\)
\(728\) −12.6774 + 12.6774i −0.469857 + 0.469857i
\(729\) −23.3508 + 13.5550i −0.864845 + 0.502038i
\(730\) 0 0
\(731\) 9.83087i 0.363608i
\(732\) −2.92236 4.17008i −0.108014 0.154131i
\(733\) 7.68183 + 7.68183i 0.283735 + 0.283735i 0.834597 0.550862i \(-0.185701\pi\)
−0.550862 + 0.834597i \(0.685701\pi\)
\(734\) 12.5714 0.464017
\(735\) 0 0
\(736\) −12.4116 −0.457497
\(737\) −35.1679 35.1679i −1.29543 1.29543i
\(738\) −0.409394 0.876152i −0.0150700 0.0322516i
\(739\) 9.51894i 0.350160i −0.984554 0.175080i \(-0.943982\pi\)
0.984554 0.175080i \(-0.0560184\pi\)
\(740\) 0 0
\(741\) 6.71467 38.1684i 0.246669 1.40215i
\(742\) −1.48247 + 1.48247i −0.0544231 + 0.0544231i
\(743\) 3.56000 3.56000i 0.130604 0.130604i −0.638783 0.769387i \(-0.720562\pi\)
0.769387 + 0.638783i \(0.220562\pi\)
\(744\) −3.28757 + 18.6876i −0.120528 + 0.685121i
\(745\) 0 0
\(746\) 20.8631i 0.763854i
\(747\) −17.2101 36.8316i −0.629683 1.34760i
\(748\) 15.9662 + 15.9662i 0.583780 + 0.583780i
\(749\) 8.95214 0.327104
\(750\) 0 0
\(751\) −27.8113 −1.01485 −0.507424 0.861696i \(-0.669402\pi\)
−0.507424 + 0.861696i \(0.669402\pi\)
\(752\) 5.34136 + 5.34136i 0.194779 + 0.194779i
\(753\) −5.31342 7.58201i −0.193632 0.276304i
\(754\) 6.91874i 0.251966i
\(755\) 0 0
\(756\) −2.46764 + 4.28573i −0.0897473 + 0.155870i
\(757\) −17.0932 + 17.0932i −0.621262 + 0.621262i −0.945854 0.324592i \(-0.894773\pi\)
0.324592 + 0.945854i \(0.394773\pi\)
\(758\) 10.3942 10.3942i 0.377534 0.377534i
\(759\) 15.9573 + 2.80724i 0.579213 + 0.101897i
\(760\) 0 0
\(761\) 19.0016i 0.688809i −0.938821 0.344404i \(-0.888081\pi\)
0.938821 0.344404i \(-0.111919\pi\)
\(762\) 7.04820 4.93933i 0.255329 0.178933i
\(763\) 4.37834 + 4.37834i 0.158507 + 0.158507i
\(764\) 23.4177 0.847221
\(765\) 0 0
\(766\) −15.8079 −0.571163
\(767\) −36.5225 36.5225i −1.31875 1.31875i
\(768\) −23.8986 + 16.7479i −0.862365 + 0.604339i
\(769\) 45.4833i 1.64017i −0.572242 0.820085i \(-0.693926\pi\)
0.572242 0.820085i \(-0.306074\pi\)
\(770\) 0 0
\(771\) −28.0063 4.92692i −1.00862 0.177439i
\(772\) −15.3754 + 15.3754i −0.553374 + 0.553374i
\(773\) 31.5448 31.5448i 1.13459 1.13459i 0.145183 0.989405i \(-0.453623\pi\)
0.989405 0.145183i \(-0.0463772\pi\)
\(774\) −4.35070 1.57966i −0.156383 0.0567797i
\(775\) 0 0
\(776\) 22.6023i 0.811376i
\(777\) 10.1893 + 14.5396i 0.365538 + 0.521606i
\(778\) 10.3708 + 10.3708i 0.371812 + 0.371812i
\(779\) 1.18750 0.0425467
\(780\) 0 0
\(781\) 38.0394 1.36116
\(782\) −12.1489 12.1489i −0.434443 0.434443i
\(783\) −1.53865 5.71540i −0.0549870 0.204252i
\(784\) 1.19072i 0.0425257i
\(785\) 0 0
\(786\) 1.18181 6.71781i 0.0421538 0.239616i
\(787\) 29.4500 29.4500i 1.04978 1.04978i 0.0510863 0.998694i \(-0.483732\pi\)
0.998694 0.0510863i \(-0.0162683\pi\)
\(788\) −16.4154 + 16.4154i −0.584774 + 0.584774i
\(789\) 1.65644 9.41576i 0.0589709 0.335210i
\(790\) 0 0
\(791\) 2.65330i 0.0943406i
\(792\) 29.8710 13.9577i 1.06142 0.495964i
\(793\) 12.9581 + 12.9581i 0.460154 + 0.460154i
\(794\) 30.5178 1.08303
\(795\) 0 0
\(796\) 16.3396 0.579141
\(797\) 12.4688 + 12.4688i 0.441668 + 0.441668i 0.892572 0.450905i \(-0.148899\pi\)
−0.450905 + 0.892572i \(0.648899\pi\)
\(798\) 3.83847 + 5.47733i 0.135880 + 0.193895i
\(799\) 41.3862i 1.46414i
\(800\) 0 0
\(801\) 15.9002 43.7924i 0.561806 1.54733i
\(802\) 7.92704 7.92704i 0.279914 0.279914i
\(803\) −2.58239 + 2.58239i −0.0911306 + 0.0911306i
\(804\) −22.2035 3.90608i −0.783056 0.137757i
\(805\) 0 0
\(806\) 22.0175i 0.775532i
\(807\) −44.2474 + 31.0082i −1.55758 + 1.09154i
\(808\) −11.8144 11.8144i −0.415628 0.415628i
\(809\) −24.8749 −0.874556 −0.437278 0.899326i \(-0.644057\pi\)
−0.437278 + 0.899326i \(0.644057\pi\)
\(810\) 0 0
\(811\) 6.91973 0.242984 0.121492 0.992592i \(-0.461232\pi\)
0.121492 + 0.992592i \(0.461232\pi\)
\(812\) −0.766585 0.766585i −0.0269019 0.0269019i
\(813\) −27.6248 + 19.3592i −0.968842 + 0.678958i
\(814\) 38.1665i 1.33774i
\(815\) 0 0
\(816\) −13.2510 2.33115i −0.463879 0.0816067i
\(817\) 4.01889 4.01889i 0.140603 0.140603i
\(818\) −14.0812 + 14.0812i −0.492337 + 0.492337i
\(819\) 6.07391 16.7288i 0.212240 0.584551i
\(820\) 0 0
\(821\) 3.31823i 0.115807i 0.998322 + 0.0579034i \(0.0184415\pi\)
−0.998322 + 0.0579034i \(0.981558\pi\)
\(822\) −19.5823 27.9431i −0.683011 0.974626i
\(823\) 8.02010 + 8.02010i 0.279563 + 0.279563i 0.832935 0.553371i \(-0.186659\pi\)
−0.553371 + 0.832935i \(0.686659\pi\)
\(824\) −7.17562 −0.249975
\(825\) 0 0
\(826\) 8.91408 0.310160
\(827\) 26.6136 + 26.6136i 0.925444 + 0.925444i 0.997407 0.0719628i \(-0.0229263\pi\)
−0.0719628 + 0.997407i \(0.522926\pi\)
\(828\) 6.65384 3.10910i 0.231237 0.108049i
\(829\) 16.8759i 0.586125i 0.956093 + 0.293062i \(0.0946744\pi\)
−0.956093 + 0.293062i \(0.905326\pi\)
\(830\) 0 0
\(831\) −0.813734 + 4.62553i −0.0282281 + 0.160458i
\(832\) 30.7133 30.7133i 1.06479 1.06479i
\(833\) −4.61300 + 4.61300i −0.159831 + 0.159831i
\(834\) −2.78179 + 15.8126i −0.0963254 + 0.547545i
\(835\) 0 0
\(836\) 13.0540i 0.451483i
\(837\) −4.89645 18.1881i −0.169246 0.628672i
\(838\) 18.7723 + 18.7723i 0.648477 + 0.648477i
\(839\) 38.5483 1.33084 0.665418 0.746471i \(-0.268253\pi\)
0.665418 + 0.746471i \(0.268253\pi\)
\(840\) 0 0
\(841\) −27.7025 −0.955258
\(842\) 4.19874 + 4.19874i 0.144698 + 0.144698i
\(843\) −0.318498 0.454482i −0.0109697 0.0156532i
\(844\) 11.8861i 0.409136i
\(845\) 0 0
\(846\) −18.3157 6.65008i −0.629706 0.228635i
\(847\) −1.57340 + 1.57340i −0.0540626 + 0.0540626i
\(848\) 1.72409 1.72409i 0.0592055 0.0592055i
\(849\) −2.91122 0.512149i −0.0999129 0.0175769i
\(850\) 0 0
\(851\) 26.3673i 0.903859i
\(852\) 14.1207 9.89570i 0.483768 0.339021i
\(853\) 18.1797 + 18.1797i 0.622462 + 0.622462i 0.946160 0.323699i \(-0.104926\pi\)
−0.323699 + 0.946160i \(0.604926\pi\)
\(854\) −3.16269 −0.108225
\(855\) 0 0
\(856\) −27.0545 −0.924704
\(857\) −32.6389 32.6389i −1.11492 1.11492i −0.992475 0.122447i \(-0.960926\pi\)
−0.122447 0.992475i \(-0.539074\pi\)
\(858\) −31.3310 + 21.9565i −1.06962 + 0.749583i
\(859\) 22.2340i 0.758615i −0.925271 0.379308i \(-0.876162\pi\)
0.925271 0.379308i \(-0.123838\pi\)
\(860\) 0 0
\(861\) 0.537092 + 0.0944864i 0.0183040 + 0.00322009i
\(862\) 10.7697 10.7697i 0.366816 0.366816i
\(863\) 41.1315 41.1315i 1.40013 1.40013i 0.600534 0.799599i \(-0.294955\pi\)
0.799599 0.600534i \(-0.205045\pi\)
\(864\) 12.5105 21.7279i 0.425616 0.739197i
\(865\) 0 0
\(866\) 26.9117i 0.914498i
\(867\) 25.4067 + 36.2542i 0.862855 + 1.23126i
\(868\) −2.43950 2.43950i −0.0828021 0.0828021i
\(869\) −26.5629 −0.901086
\(870\) 0 0
\(871\) 81.1325 2.74907
\(872\) −13.2319 13.2319i −0.448089 0.448089i
\(873\) 9.49818 + 20.3272i 0.321465 + 0.687972i
\(874\) 9.93300i 0.335989i
\(875\) 0 0
\(876\) −0.286825 + 1.63041i −0.00969092 + 0.0550864i
\(877\) 11.3627 11.3627i 0.383690 0.383690i −0.488740 0.872430i \(-0.662543\pi\)
0.872430 + 0.488740i \(0.162543\pi\)
\(878\) −11.3437 + 11.3437i −0.382831 + 0.382831i
\(879\) −4.75397 + 27.0231i −0.160347 + 0.911467i
\(880\) 0 0
\(881\) 15.3402i 0.516823i 0.966035 + 0.258412i \(0.0831991\pi\)
−0.966035 + 0.258412i \(0.916801\pi\)
\(882\) 1.30027 + 2.78274i 0.0437825 + 0.0936998i
\(883\) −0.509152 0.509152i −0.0171343 0.0171343i 0.698488 0.715622i \(-0.253857\pi\)
−0.715622 + 0.698488i \(0.753857\pi\)
\(884\) −36.8340 −1.23886
\(885\) 0 0
\(886\) 25.2344 0.847767
\(887\) −35.3019 35.3019i −1.18532 1.18532i −0.978346 0.206974i \(-0.933638\pi\)
−0.206974 0.978346i \(-0.566362\pi\)
\(888\) −30.7933 43.9406i −1.03335 1.47455i
\(889\) 4.85330i 0.162775i
\(890\) 0 0
\(891\) −20.9989 + 25.1054i −0.703488 + 0.841063i
\(892\) −13.9621 + 13.9621i −0.467487 + 0.467487i
\(893\) 16.9188 16.9188i 0.566167 0.566167i
\(894\) −35.9781 6.32934i −1.20329 0.211685i
\(895\) 0 0
\(896\) 2.15404i 0.0719613i
\(897\) −21.6450 + 15.1686i −0.722704 + 0.506466i
\(898\) 0.449443 + 0.449443i 0.0149981 + 0.0149981i
\(899\) 4.12912 0.137714
\(900\) 0 0
\(901\) −13.3587 −0.445042
\(902\) −0.828946 0.828946i −0.0276009 0.0276009i
\(903\) 2.13747 1.49792i 0.0711304 0.0498477i
\(904\) 8.01862i 0.266695i
\(905\) 0 0
\(906\) −27.8192 4.89401i −0.924229 0.162593i
\(907\) 6.84363 6.84363i 0.227239 0.227239i −0.584299 0.811538i \(-0.698631\pi\)
0.811538 + 0.584299i \(0.198631\pi\)
\(908\) 1.51321 1.51321i 0.0502177 0.0502177i
\(909\) 15.5899 + 5.66041i 0.517085 + 0.187744i
\(910\) 0 0
\(911\) 33.2065i 1.10018i −0.835105 0.550090i \(-0.814593\pi\)
0.835105 0.550090i \(-0.185407\pi\)
\(912\) −4.46409 6.37006i −0.147821 0.210934i
\(913\) −34.8472 34.8472i −1.15327 1.15327i
\(914\) −13.1902 −0.436293
\(915\) 0 0
\(916\) 1.29123 0.0426636
\(917\) 2.71979 + 2.71979i 0.0898154 + 0.0898154i
\(918\) 33.5136 9.02227i 1.10611 0.297779i
\(919\) 48.0196i 1.58402i 0.610507 + 0.792011i \(0.290966\pi\)
−0.610507 + 0.792011i \(0.709034\pi\)
\(920\) 0 0
\(921\) −6.81543 + 38.7411i −0.224576 + 1.27656i
\(922\) 2.01462 2.01462i 0.0663479 0.0663479i
\(923\) −43.8786 + 43.8786i −1.44428 + 1.44428i
\(924\) −1.03868 + 5.90417i −0.0341699 + 0.194233i
\(925\) 0 0
\(926\) 15.1261i 0.497073i
\(927\) 6.45334 3.01541i 0.211955 0.0990391i
\(928\) 3.88645 + 3.88645i 0.127579 + 0.127579i
\(929\) 29.7649 0.976555 0.488277 0.872688i \(-0.337625\pi\)
0.488277 + 0.872688i \(0.337625\pi\)
\(930\) 0 0
\(931\) −3.77162 −0.123610
\(932\) 14.3978 + 14.3978i 0.471615 + 0.471615i
\(933\) 0.705751 + 1.00708i 0.0231053 + 0.0329702i
\(934\) 23.1265i 0.756722i
\(935\) 0 0
\(936\) −18.3561 + 50.5565i −0.599989 + 1.65249i
\(937\) −16.2931 + 16.2931i −0.532273 + 0.532273i −0.921248 0.388975i \(-0.872829\pi\)
0.388975 + 0.921248i \(0.372829\pi\)
\(938\) −9.90105 + 9.90105i −0.323281 + 0.323281i
\(939\) 36.0493 + 6.34187i 1.17642 + 0.206959i
\(940\) 0 0
\(941\) 38.9179i 1.26869i 0.773052 + 0.634343i \(0.218729\pi\)
−0.773052 + 0.634343i \(0.781271\pi\)
\(942\) 8.22767 5.76589i 0.268072 0.187863i
\(943\) −0.572676 0.572676i −0.0186489 0.0186489i
\(944\) −10.3670 −0.337416
\(945\) 0 0
\(946\) −5.61085 −0.182424
\(947\) −2.32343 2.32343i −0.0755014 0.0755014i 0.668348 0.743849i \(-0.267002\pi\)
−0.743849 + 0.668348i \(0.767002\pi\)
\(948\) −9.86050 + 6.91017i −0.320254 + 0.224432i
\(949\) 5.95759i 0.193392i
\(950\) 0 0
\(951\) −9.26198 1.62939i −0.300340 0.0528366i
\(952\) 13.9411 13.9411i 0.451833 0.451833i
\(953\) 4.77849 4.77849i 0.154791 0.154791i −0.625463 0.780254i \(-0.715090\pi\)
0.780254 + 0.625463i \(0.215090\pi\)
\(954\) −2.14652 + 5.91195i −0.0694962 + 0.191407i
\(955\) 0 0
\(956\) 11.8956i 0.384732i
\(957\) −4.11769 5.87576i −0.133106 0.189936i
\(958\) −7.88727 7.88727i −0.254826 0.254826i
\(959\) 19.2412 0.621332
\(960\) 0 0
\(961\) −17.8599 −0.576127
\(962\) 44.0252 + 44.0252i 1.41943 + 1.41943i
\(963\) 24.3313 11.3691i 0.784064 0.366365i
\(964\) 17.1668i 0.552904i
\(965\) 0 0
\(966\) 0.790343 4.49257i 0.0254289 0.144546i
\(967\) −26.7726 + 26.7726i −0.860949 + 0.860949i −0.991448 0.130499i \(-0.958342\pi\)
0.130499 + 0.991448i \(0.458342\pi\)
\(968\) 4.75501 4.75501i 0.152832 0.152832i
\(969\) −7.38396 + 41.9728i −0.237207 + 1.34836i
\(970\) 0 0
\(971\) 10.3583i 0.332413i −0.986091 0.166206i \(-0.946848\pi\)
0.986091 0.166206i \(-0.0531518\pi\)
\(972\) −1.26404 + 14.7822i −0.0405442 + 0.474139i
\(973\) −6.40193 6.40193i −0.205236 0.205236i
\(974\) −7.28874 −0.233546
\(975\) 0 0
\(976\) 3.67816 0.117735
\(977\) 11.0435 + 11.0435i 0.353311 + 0.353311i 0.861340 0.508029i \(-0.169626\pi\)
−0.508029 + 0.861340i \(0.669626\pi\)
\(978\) −7.45889 10.6435i −0.238509 0.340342i
\(979\) 56.4765i 1.80500i
\(980\) 0 0
\(981\) 17.4605 + 6.33957i 0.557470 + 0.202407i
\(982\) 8.62939 8.62939i 0.275375 0.275375i
\(983\) −9.03917 + 9.03917i −0.288305 + 0.288305i −0.836410 0.548105i \(-0.815349\pi\)
0.548105 + 0.836410i \(0.315349\pi\)
\(984\) −1.62316 0.285550i −0.0517444 0.00910300i
\(985\) 0 0
\(986\) 7.60837i 0.242300i
\(987\) 8.99835 6.30598i 0.286421 0.200721i
\(988\) −15.0579 15.0579i −0.479055 0.479055i
\(989\) −3.87624 −0.123257
\(990\) 0 0
\(991\) 9.41165 0.298971 0.149485 0.988764i \(-0.452238\pi\)
0.149485 + 0.988764i \(0.452238\pi\)
\(992\) 12.3678 + 12.3678i 0.392679 + 0.392679i
\(993\) 45.1169 31.6176i 1.43174 1.00335i
\(994\) 10.7095i 0.339685i
\(995\) 0 0
\(996\) −22.0010 3.87046i −0.697128 0.122640i
\(997\) −14.3463 + 14.3463i −0.454351 + 0.454351i −0.896796 0.442445i \(-0.854111\pi\)
0.442445 + 0.896796i \(0.354111\pi\)
\(998\) −0.699929 + 0.699929i −0.0221559 + 0.0221559i
\(999\) 46.1589 + 26.5774i 1.46040 + 0.840872i
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 525.2.j.c.218.8 yes 32
3.2 odd 2 inner 525.2.j.c.218.10 yes 32
5.2 odd 4 inner 525.2.j.c.407.10 yes 32
5.3 odd 4 inner 525.2.j.c.407.7 yes 32
5.4 even 2 inner 525.2.j.c.218.9 yes 32
15.2 even 4 inner 525.2.j.c.407.8 yes 32
15.8 even 4 inner 525.2.j.c.407.9 yes 32
15.14 odd 2 inner 525.2.j.c.218.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.j.c.218.7 32 15.14 odd 2 inner
525.2.j.c.218.8 yes 32 1.1 even 1 trivial
525.2.j.c.218.9 yes 32 5.4 even 2 inner
525.2.j.c.218.10 yes 32 3.2 odd 2 inner
525.2.j.c.407.7 yes 32 5.3 odd 4 inner
525.2.j.c.407.8 yes 32 15.2 even 4 inner
525.2.j.c.407.9 yes 32 15.8 even 4 inner
525.2.j.c.407.10 yes 32 5.2 odd 4 inner