Properties

Label 847.2.f.w.148.4
Level $847$
Weight $2$
Character 847.148
Analytic conductor $6.763$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 148.4
Root \(1.60551 - 1.16647i\) of defining polynomial
Character \(\chi\) \(=\) 847.148
Dual form 847.2.f.w.372.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.613249 + 1.88739i) q^{2} +(-2.25424 - 1.63780i) q^{3} +(-1.56812 + 1.13930i) q^{4} +(-0.00832008 + 0.0256066i) q^{5} +(1.70875 - 5.25900i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.0990607 + 0.0719718i) q^{8} +(1.47215 + 4.53082i) q^{9} +O(q^{10})\) \(q+(0.613249 + 1.88739i) q^{2} +(-2.25424 - 1.63780i) q^{3} +(-1.56812 + 1.13930i) q^{4} +(-0.00832008 + 0.0256066i) q^{5} +(1.70875 - 5.25900i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.0990607 + 0.0719718i) q^{8} +(1.47215 + 4.53082i) q^{9} -0.0534317 q^{10} +5.40087 q^{12} +(-1.50835 - 4.64222i) q^{13} +(-1.60551 - 1.16647i) q^{14} +(0.0606939 - 0.0440967i) q^{15} +(-1.27302 + 3.91797i) q^{16} +(0.518771 - 1.59661i) q^{17} +(-7.64861 + 5.55704i) q^{18} +(-1.11154 - 0.807582i) q^{19} +(-0.0161268 - 0.0496332i) q^{20} +2.78639 q^{21} +8.06246 q^{23} +(-0.105431 - 0.324483i) q^{24} +(4.04450 + 2.93850i) q^{25} +(7.83667 - 5.69367i) q^{26} +(1.51887 - 4.67460i) q^{27} +(0.598967 - 1.84343i) q^{28} +(5.17218 - 3.75781i) q^{29} +(0.120448 + 0.0875106i) q^{30} +(1.23933 + 3.81425i) q^{31} -7.93050 q^{32} +3.33156 q^{34} +(-0.00832008 - 0.0256066i) q^{35} +(-7.47049 - 5.42763i) q^{36} +(-0.421528 + 0.306258i) q^{37} +(0.842568 - 2.59316i) q^{38} +(-4.20285 + 12.9351i) q^{39} +(-0.00266714 + 0.00193779i) q^{40} +(8.57456 + 6.22978i) q^{41} +(1.70875 + 5.25900i) q^{42} +3.73968 q^{43} -0.128267 q^{45} +(4.94430 + 15.2170i) q^{46} +(7.24804 + 5.26601i) q^{47} +(9.28655 - 6.74708i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.06580 + 9.43556i) q^{50} +(-3.78437 + 2.74951i) q^{51} +(7.65417 + 5.56108i) q^{52} +(-1.22388 - 3.76673i) q^{53} +9.75422 q^{54} -0.122446 q^{56} +(1.18302 + 3.64097i) q^{57} +(10.2643 + 7.45742i) q^{58} +(-7.87191 + 5.71928i) q^{59} +(-0.0449356 + 0.138298i) q^{60} +(2.61652 - 8.05281i) q^{61} +(-6.43895 + 4.67817i) q^{62} +(-3.85415 - 2.80020i) q^{63} +(-2.31732 - 7.13199i) q^{64} +0.131421 q^{65} +2.81285 q^{67} +(1.00553 + 3.09472i) q^{68} +(-18.1747 - 13.2047i) q^{69} +(0.0432272 - 0.0314064i) q^{70} +(0.632097 - 1.94539i) q^{71} +(-0.180259 + 0.554780i) q^{72} +(8.46987 - 6.15372i) q^{73} +(-0.836529 - 0.607774i) q^{74} +(-4.30459 - 13.2482i) q^{75} +2.66311 q^{76} -26.9908 q^{78} +(1.80936 + 5.56864i) q^{79} +(-0.0897340 - 0.0651956i) q^{80} +(0.482477 - 0.350540i) q^{81} +(-6.49967 + 20.0039i) q^{82} +(0.805136 - 2.47795i) q^{83} +(-4.36939 + 3.17455i) q^{84} +(0.0365676 + 0.0265679i) q^{85} +(2.29336 + 7.05823i) q^{86} -17.8139 q^{87} +1.21791 q^{89} +(-0.0786597 - 0.242090i) q^{90} +(3.94891 + 2.86905i) q^{91} +(-12.6429 + 9.18560i) q^{92} +(3.45325 - 10.6280i) q^{93} +(-5.49414 + 16.9092i) q^{94} +(0.0299275 - 0.0217436i) q^{95} +(17.8773 + 12.9886i) q^{96} +(1.04964 + 3.23046i) q^{97} +1.98451 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.613249 + 1.88739i 0.433632 + 1.33458i 0.894482 + 0.447105i \(0.147545\pi\)
−0.460849 + 0.887478i \(0.652455\pi\)
\(3\) −2.25424 1.63780i −1.30149 0.945585i −0.301517 0.953461i \(-0.597493\pi\)
−0.999969 + 0.00787594i \(0.997493\pi\)
\(4\) −1.56812 + 1.13930i −0.784059 + 0.569652i
\(5\) −0.00832008 + 0.0256066i −0.00372085 + 0.0114516i −0.952900 0.303286i \(-0.901916\pi\)
0.949179 + 0.314737i \(0.101916\pi\)
\(6\) 1.70875 5.25900i 0.697595 2.14698i
\(7\) −0.809017 + 0.587785i −0.305780 + 0.222162i
\(8\) 0.0990607 + 0.0719718i 0.0350232 + 0.0254459i
\(9\) 1.47215 + 4.53082i 0.490718 + 1.51027i
\(10\) −0.0534317 −0.0168966
\(11\) 0 0
\(12\) 5.40087 1.55910
\(13\) −1.50835 4.64222i −0.418341 1.28752i −0.909229 0.416297i \(-0.863328\pi\)
0.490888 0.871223i \(-0.336672\pi\)
\(14\) −1.60551 1.16647i −0.429090 0.311752i
\(15\) 0.0606939 0.0440967i 0.0156711 0.0113857i
\(16\) −1.27302 + 3.91797i −0.318256 + 0.979492i
\(17\) 0.518771 1.59661i 0.125821 0.387236i −0.868229 0.496163i \(-0.834742\pi\)
0.994050 + 0.108928i \(0.0347417\pi\)
\(18\) −7.64861 + 5.55704i −1.80280 + 1.30981i
\(19\) −1.11154 0.807582i −0.255005 0.185272i 0.452937 0.891543i \(-0.350376\pi\)
−0.707942 + 0.706270i \(0.750376\pi\)
\(20\) −0.0161268 0.0496332i −0.00360606 0.0110983i
\(21\) 2.78639 0.608041
\(22\) 0 0
\(23\) 8.06246 1.68114 0.840570 0.541703i \(-0.182220\pi\)
0.840570 + 0.541703i \(0.182220\pi\)
\(24\) −0.105431 0.324483i −0.0215210 0.0662349i
\(25\) 4.04450 + 2.93850i 0.808900 + 0.587700i
\(26\) 7.83667 5.69367i 1.53690 1.11662i
\(27\) 1.51887 4.67460i 0.292307 0.899628i
\(28\) 0.598967 1.84343i 0.113194 0.348376i
\(29\) 5.17218 3.75781i 0.960449 0.697807i 0.00719396 0.999974i \(-0.497710\pi\)
0.953255 + 0.302167i \(0.0977101\pi\)
\(30\) 0.120448 + 0.0875106i 0.0219907 + 0.0159772i
\(31\) 1.23933 + 3.81425i 0.222589 + 0.685060i 0.998527 + 0.0542506i \(0.0172770\pi\)
−0.775938 + 0.630809i \(0.782723\pi\)
\(32\) −7.93050 −1.40193
\(33\) 0 0
\(34\) 3.33156 0.571358
\(35\) −0.00832008 0.0256066i −0.00140635 0.00432830i
\(36\) −7.47049 5.42763i −1.24508 0.904605i
\(37\) −0.421528 + 0.306258i −0.0692988 + 0.0503486i −0.621895 0.783100i \(-0.713637\pi\)
0.552596 + 0.833449i \(0.313637\pi\)
\(38\) 0.842568 2.59316i 0.136683 0.420665i
\(39\) −4.20285 + 12.9351i −0.672995 + 2.07127i
\(40\) −0.00266714 + 0.00193779i −0.000421712 + 0.000306392i
\(41\) 8.57456 + 6.22978i 1.33912 + 0.972929i 0.999476 + 0.0323754i \(0.0103072\pi\)
0.339646 + 0.940553i \(0.389693\pi\)
\(42\) 1.70875 + 5.25900i 0.263666 + 0.811481i
\(43\) 3.73968 0.570296 0.285148 0.958483i \(-0.407957\pi\)
0.285148 + 0.958483i \(0.407957\pi\)
\(44\) 0 0
\(45\) −0.128267 −0.0191209
\(46\) 4.94430 + 15.2170i 0.728997 + 2.24362i
\(47\) 7.24804 + 5.26601i 1.05723 + 0.768126i 0.973575 0.228368i \(-0.0733391\pi\)
0.0836598 + 0.996494i \(0.473339\pi\)
\(48\) 9.28655 6.74708i 1.34040 0.973856i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) −3.06580 + 9.43556i −0.433570 + 1.33439i
\(51\) −3.78437 + 2.74951i −0.529918 + 0.385008i
\(52\) 7.65417 + 5.56108i 1.06144 + 0.771183i
\(53\) −1.22388 3.76673i −0.168114 0.517400i 0.831139 0.556065i \(-0.187689\pi\)
−0.999252 + 0.0386649i \(0.987689\pi\)
\(54\) 9.75422 1.32738
\(55\) 0 0
\(56\) −0.122446 −0.0163625
\(57\) 1.18302 + 3.64097i 0.156695 + 0.482258i
\(58\) 10.2643 + 7.45742i 1.34776 + 0.979207i
\(59\) −7.87191 + 5.71928i −1.02484 + 0.744587i −0.967269 0.253755i \(-0.918334\pi\)
−0.0575670 + 0.998342i \(0.518334\pi\)
\(60\) −0.0449356 + 0.138298i −0.00580116 + 0.0178541i
\(61\) 2.61652 8.05281i 0.335011 1.03106i −0.631706 0.775208i \(-0.717645\pi\)
0.966717 0.255849i \(-0.0823549\pi\)
\(62\) −6.43895 + 4.67817i −0.817747 + 0.594128i
\(63\) −3.85415 2.80020i −0.485577 0.352792i
\(64\) −2.31732 7.13199i −0.289665 0.891499i
\(65\) 0.131421 0.0163008
\(66\) 0 0
\(67\) 2.81285 0.343644 0.171822 0.985128i \(-0.445035\pi\)
0.171822 + 0.985128i \(0.445035\pi\)
\(68\) 1.00553 + 3.09472i 0.121939 + 0.375289i
\(69\) −18.1747 13.2047i −2.18798 1.58966i
\(70\) 0.0432272 0.0314064i 0.00516664 0.00375378i
\(71\) 0.632097 1.94539i 0.0750161 0.230876i −0.906517 0.422170i \(-0.861268\pi\)
0.981533 + 0.191294i \(0.0612685\pi\)
\(72\) −0.180259 + 0.554780i −0.0212437 + 0.0653814i
\(73\) 8.46987 6.15372i 0.991323 0.720238i 0.0311128 0.999516i \(-0.490095\pi\)
0.960210 + 0.279277i \(0.0900949\pi\)
\(74\) −0.836529 0.607774i −0.0972446 0.0706523i
\(75\) −4.30459 13.2482i −0.497051 1.52977i
\(76\) 2.66311 0.305479
\(77\) 0 0
\(78\) −26.9908 −3.05611
\(79\) 1.80936 + 5.56864i 0.203569 + 0.626521i 0.999769 + 0.0214875i \(0.00684021\pi\)
−0.796200 + 0.605033i \(0.793160\pi\)
\(80\) −0.0897340 0.0651956i −0.0100326 0.00728909i
\(81\) 0.482477 0.350540i 0.0536086 0.0389489i
\(82\) −6.49967 + 20.0039i −0.717768 + 2.20906i
\(83\) 0.805136 2.47795i 0.0883752 0.271991i −0.897095 0.441837i \(-0.854327\pi\)
0.985471 + 0.169846i \(0.0543270\pi\)
\(84\) −4.36939 + 3.17455i −0.476740 + 0.346372i
\(85\) 0.0365676 + 0.0265679i 0.00396631 + 0.00288169i
\(86\) 2.29336 + 7.05823i 0.247299 + 0.761108i
\(87\) −17.8139 −1.90985
\(88\) 0 0
\(89\) 1.21791 0.129099 0.0645493 0.997915i \(-0.479439\pi\)
0.0645493 + 0.997915i \(0.479439\pi\)
\(90\) −0.0786597 0.242090i −0.00829146 0.0255185i
\(91\) 3.94891 + 2.86905i 0.413958 + 0.300758i
\(92\) −12.6429 + 9.18560i −1.31811 + 0.957665i
\(93\) 3.45325 10.6280i 0.358085 1.10207i
\(94\) −5.49414 + 16.9092i −0.566677 + 1.74405i
\(95\) 0.0299275 0.0217436i 0.00307050 0.00223085i
\(96\) 17.8773 + 12.9886i 1.82459 + 1.32564i
\(97\) 1.04964 + 3.23046i 0.106575 + 0.328003i 0.990097 0.140386i \(-0.0448344\pi\)
−0.883522 + 0.468389i \(0.844834\pi\)
\(98\) 1.98451 0.200466
\(99\) 0 0
\(100\) −9.69009 −0.969009
\(101\) −1.25101 3.85021i −0.124480 0.383111i 0.869326 0.494239i \(-0.164553\pi\)
−0.993806 + 0.111129i \(0.964553\pi\)
\(102\) −7.51014 5.45644i −0.743615 0.540268i
\(103\) 3.19802 2.32350i 0.315110 0.228941i −0.418976 0.907997i \(-0.637611\pi\)
0.734086 + 0.679056i \(0.237611\pi\)
\(104\) 0.184691 0.568420i 0.0181104 0.0557382i
\(105\) −0.0231830 + 0.0713500i −0.00226243 + 0.00696304i
\(106\) 6.35873 4.61989i 0.617614 0.448723i
\(107\) −8.41265 6.11215i −0.813281 0.590883i 0.101499 0.994836i \(-0.467636\pi\)
−0.914780 + 0.403952i \(0.867636\pi\)
\(108\) 2.94403 + 9.06078i 0.283289 + 0.871874i
\(109\) −3.77697 −0.361768 −0.180884 0.983504i \(-0.557896\pi\)
−0.180884 + 0.983504i \(0.557896\pi\)
\(110\) 0 0
\(111\) 1.45182 0.137800
\(112\) −1.27302 3.91797i −0.120290 0.370213i
\(113\) −5.13619 3.73166i −0.483173 0.351045i 0.319380 0.947627i \(-0.396525\pi\)
−0.802553 + 0.596581i \(0.796525\pi\)
\(114\) −6.14642 + 4.46564i −0.575665 + 0.418245i
\(115\) −0.0670803 + 0.206452i −0.00625527 + 0.0192517i
\(116\) −3.82930 + 11.7854i −0.355541 + 1.09424i
\(117\) 18.8126 13.6681i 1.73922 1.26362i
\(118\) −15.6219 11.3500i −1.43811 1.04485i
\(119\) 0.518771 + 1.59661i 0.0475557 + 0.146361i
\(120\) 0.00918610 0.000838572
\(121\) 0 0
\(122\) 16.8033 1.52130
\(123\) −9.12597 28.0869i −0.822861 2.53251i
\(124\) −6.28900 4.56923i −0.564769 0.410329i
\(125\) −0.217807 + 0.158246i −0.0194812 + 0.0141539i
\(126\) 2.92151 8.99149i 0.260269 0.801025i
\(127\) −1.55475 + 4.78503i −0.137962 + 0.424603i −0.996039 0.0889179i \(-0.971659\pi\)
0.858077 + 0.513521i \(0.171659\pi\)
\(128\) −0.792108 + 0.575500i −0.0700131 + 0.0508675i
\(129\) −8.43014 6.12486i −0.742233 0.539264i
\(130\) 0.0805937 + 0.248042i 0.00706853 + 0.0217547i
\(131\) −3.76357 −0.328825 −0.164412 0.986392i \(-0.552573\pi\)
−0.164412 + 0.986392i \(0.552573\pi\)
\(132\) 0 0
\(133\) 1.37394 0.119136
\(134\) 1.72498 + 5.30893i 0.149015 + 0.458622i
\(135\) 0.107063 + 0.0777861i 0.00921455 + 0.00669476i
\(136\) 0.166301 0.120825i 0.0142602 0.0103606i
\(137\) 5.91393 18.2012i 0.505261 1.55503i −0.295071 0.955475i \(-0.595343\pi\)
0.800332 0.599557i \(-0.204657\pi\)
\(138\) 13.7768 42.4005i 1.17276 3.60937i
\(139\) −2.84053 + 2.06376i −0.240930 + 0.175046i −0.701698 0.712475i \(-0.747574\pi\)
0.460767 + 0.887521i \(0.347574\pi\)
\(140\) 0.0422205 + 0.0306750i 0.00356828 + 0.00259251i
\(141\) −7.71414 23.7417i −0.649648 1.99941i
\(142\) 4.05934 0.340652
\(143\) 0 0
\(144\) −19.6257 −1.63548
\(145\) 0.0531916 + 0.163707i 0.00441732 + 0.0135951i
\(146\) 16.8086 + 12.2121i 1.39109 + 1.01068i
\(147\) −2.25424 + 1.63780i −0.185927 + 0.135084i
\(148\) 0.312085 0.960498i 0.0256532 0.0789524i
\(149\) −0.966119 + 2.97341i −0.0791476 + 0.243591i −0.982799 0.184677i \(-0.940876\pi\)
0.903652 + 0.428268i \(0.140876\pi\)
\(150\) 22.3646 16.2488i 1.82606 1.32671i
\(151\) −15.9550 11.5920i −1.29840 0.943343i −0.298462 0.954421i \(-0.596474\pi\)
−0.999939 + 0.0110780i \(0.996474\pi\)
\(152\) −0.0519869 0.159999i −0.00421669 0.0129777i
\(153\) 7.99769 0.646575
\(154\) 0 0
\(155\) −0.107981 −0.00867326
\(156\) −8.14639 25.0720i −0.652233 2.00737i
\(157\) 18.5706 + 13.4924i 1.48210 + 1.07681i 0.976873 + 0.213820i \(0.0685907\pi\)
0.505226 + 0.862987i \(0.331409\pi\)
\(158\) −9.40058 + 6.82992i −0.747870 + 0.543359i
\(159\) −3.41022 + 10.4956i −0.270448 + 0.832355i
\(160\) 0.0659824 0.203073i 0.00521637 0.0160543i
\(161\) −6.52267 + 4.73900i −0.514058 + 0.373485i
\(162\) 0.957483 + 0.695652i 0.0752270 + 0.0546556i
\(163\) 5.86795 + 18.0597i 0.459613 + 1.41454i 0.865633 + 0.500680i \(0.166917\pi\)
−0.406019 + 0.913864i \(0.633083\pi\)
\(164\) −20.5435 −1.60418
\(165\) 0 0
\(166\) 5.17061 0.401317
\(167\) −0.933366 2.87260i −0.0722260 0.222289i 0.908427 0.418044i \(-0.137284\pi\)
−0.980653 + 0.195755i \(0.937284\pi\)
\(168\) 0.276022 + 0.200542i 0.0212956 + 0.0154721i
\(169\) −8.75787 + 6.36296i −0.673682 + 0.489459i
\(170\) −0.0277189 + 0.0853099i −0.00212594 + 0.00654297i
\(171\) 2.02265 6.22508i 0.154676 0.476044i
\(172\) −5.86426 + 4.26064i −0.447146 + 0.324870i
\(173\) −7.14871 5.19384i −0.543506 0.394880i 0.281879 0.959450i \(-0.409042\pi\)
−0.825386 + 0.564569i \(0.809042\pi\)
\(174\) −10.9243 33.6216i −0.828171 2.54885i
\(175\) −4.99928 −0.377910
\(176\) 0 0
\(177\) 27.1122 2.03788
\(178\) 0.746884 + 2.29867i 0.0559813 + 0.172293i
\(179\) −6.84779 4.97521i −0.511828 0.371865i 0.301689 0.953407i \(-0.402450\pi\)
−0.813517 + 0.581542i \(0.802450\pi\)
\(180\) 0.201138 0.146135i 0.0149919 0.0108923i
\(181\) −7.47846 + 23.0163i −0.555869 + 1.71079i 0.137767 + 0.990465i \(0.456007\pi\)
−0.693637 + 0.720325i \(0.743993\pi\)
\(182\) −2.99334 + 9.21255i −0.221881 + 0.682880i
\(183\) −19.0872 + 13.8676i −1.41096 + 1.02512i
\(184\) 0.798673 + 0.580270i 0.0588790 + 0.0427781i
\(185\) −0.00433507 0.0133420i −0.000318721 0.000980922i
\(186\) 22.1769 1.62609
\(187\) 0 0
\(188\) −17.3653 −1.26650
\(189\) 1.51887 + 4.67460i 0.110482 + 0.340027i
\(190\) 0.0593916 + 0.0431505i 0.00430872 + 0.00313047i
\(191\) 6.29996 4.57719i 0.455849 0.331194i −0.336052 0.941844i \(-0.609092\pi\)
0.791901 + 0.610650i \(0.209092\pi\)
\(192\) −6.45698 + 19.8725i −0.465992 + 1.43418i
\(193\) 5.27296 16.2285i 0.379556 1.16815i −0.560797 0.827953i \(-0.689505\pi\)
0.940353 0.340200i \(-0.110495\pi\)
\(194\) −5.45343 + 3.96215i −0.391533 + 0.284466i
\(195\) −0.296254 0.215241i −0.0212152 0.0154137i
\(196\) 0.598967 + 1.84343i 0.0427834 + 0.131674i
\(197\) −6.05536 −0.431426 −0.215713 0.976457i \(-0.569208\pi\)
−0.215713 + 0.976457i \(0.569208\pi\)
\(198\) 0 0
\(199\) −13.7181 −0.972451 −0.486226 0.873833i \(-0.661627\pi\)
−0.486226 + 0.873833i \(0.661627\pi\)
\(200\) 0.189162 + 0.582180i 0.0133757 + 0.0411663i
\(201\) −6.34083 4.60688i −0.447248 0.324945i
\(202\) 6.49966 4.72228i 0.457314 0.332258i
\(203\) −1.97560 + 6.08026i −0.138660 + 0.426750i
\(204\) 2.80181 8.62310i 0.196166 0.603737i
\(205\) −0.230864 + 0.167733i −0.0161243 + 0.0117150i
\(206\) 6.34652 + 4.61101i 0.442183 + 0.321265i
\(207\) 11.8692 + 36.5296i 0.824965 + 2.53898i
\(208\) 20.1082 1.39425
\(209\) 0 0
\(210\) −0.148882 −0.0102738
\(211\) 5.57320 + 17.1525i 0.383675 + 1.18083i 0.937437 + 0.348155i \(0.113192\pi\)
−0.553762 + 0.832675i \(0.686808\pi\)
\(212\) 6.21065 + 4.51230i 0.426549 + 0.309906i
\(213\) −4.61107 + 3.35014i −0.315945 + 0.229548i
\(214\) 6.37693 19.6262i 0.435918 1.34162i
\(215\) −0.0311145 + 0.0957604i −0.00212199 + 0.00653081i
\(216\) 0.486900 0.353753i 0.0331293 0.0240699i
\(217\) −3.24460 2.35734i −0.220258 0.160026i
\(218\) −2.31622 7.12860i −0.156874 0.482810i
\(219\) −29.1717 −1.97124
\(220\) 0 0
\(221\) −8.19432 −0.551210
\(222\) 0.890325 + 2.74014i 0.0597547 + 0.183906i
\(223\) 5.28542 + 3.84008i 0.353938 + 0.257151i 0.750519 0.660849i \(-0.229803\pi\)
−0.396581 + 0.918000i \(0.629803\pi\)
\(224\) 6.41591 4.66143i 0.428681 0.311455i
\(225\) −7.35970 + 22.6508i −0.490647 + 1.51006i
\(226\) 3.89332 11.9824i 0.258980 0.797059i
\(227\) −11.0089 + 7.99841i −0.730684 + 0.530873i −0.889780 0.456390i \(-0.849142\pi\)
0.159096 + 0.987263i \(0.449142\pi\)
\(228\) −6.00329 4.36164i −0.397577 0.288857i
\(229\) −6.00144 18.4705i −0.396586 1.22057i −0.927719 0.373279i \(-0.878233\pi\)
0.531133 0.847289i \(-0.321767\pi\)
\(230\) −0.430791 −0.0284055
\(231\) 0 0
\(232\) 0.782815 0.0513943
\(233\) 1.34778 + 4.14803i 0.0882959 + 0.271747i 0.985449 0.169974i \(-0.0543683\pi\)
−0.897153 + 0.441721i \(0.854368\pi\)
\(234\) 37.3338 + 27.1246i 2.44059 + 1.77319i
\(235\) −0.195149 + 0.141784i −0.0127301 + 0.00924895i
\(236\) 5.82808 17.9370i 0.379376 1.16760i
\(237\) 5.04159 15.5164i 0.327486 1.00790i
\(238\) −2.69529 + 1.95824i −0.174710 + 0.126934i
\(239\) −8.56758 6.22471i −0.554191 0.402643i 0.275137 0.961405i \(-0.411277\pi\)
−0.829328 + 0.558762i \(0.811277\pi\)
\(240\) 0.0955046 + 0.293933i 0.00616479 + 0.0189733i
\(241\) 18.6887 1.20384 0.601921 0.798555i \(-0.294402\pi\)
0.601921 + 0.798555i \(0.294402\pi\)
\(242\) 0 0
\(243\) −16.4072 −1.05252
\(244\) 5.07159 + 15.6088i 0.324675 + 0.999248i
\(245\) 0.0217822 + 0.0158257i 0.00139162 + 0.00101107i
\(246\) 47.4142 34.4485i 3.02302 2.19635i
\(247\) −2.07238 + 6.37813i −0.131862 + 0.405831i
\(248\) −0.151750 + 0.467039i −0.00963614 + 0.0296570i
\(249\) −5.87337 + 4.26725i −0.372210 + 0.270426i
\(250\) −0.432241 0.314041i −0.0273373 0.0198617i
\(251\) 5.86612 + 18.0541i 0.370266 + 1.13956i 0.946617 + 0.322360i \(0.104476\pi\)
−0.576351 + 0.817202i \(0.695524\pi\)
\(252\) 9.23404 0.581690
\(253\) 0 0
\(254\) −9.98465 −0.626493
\(255\) −0.0389191 0.119781i −0.00243721 0.00750097i
\(256\) −13.7056 9.95771i −0.856601 0.622357i
\(257\) 11.0908 8.05797i 0.691828 0.502643i −0.185432 0.982657i \(-0.559369\pi\)
0.877261 + 0.480014i \(0.159369\pi\)
\(258\) 6.39019 19.6670i 0.397836 1.22441i
\(259\) 0.161010 0.495536i 0.0100046 0.0307911i
\(260\) −0.206083 + 0.149728i −0.0127807 + 0.00928575i
\(261\) 24.6402 + 17.9021i 1.52519 + 1.10811i
\(262\) −2.30801 7.10332i −0.142589 0.438844i
\(263\) 16.5767 1.02217 0.511083 0.859531i \(-0.329244\pi\)
0.511083 + 0.859531i \(0.329244\pi\)
\(264\) 0 0
\(265\) 0.106636 0.00655059
\(266\) 0.842568 + 2.59316i 0.0516611 + 0.158997i
\(267\) −2.74547 1.99470i −0.168020 0.122074i
\(268\) −4.41087 + 3.20469i −0.269437 + 0.195757i
\(269\) −2.64012 + 8.12546i −0.160971 + 0.495418i −0.998717 0.0506426i \(-0.983873\pi\)
0.837746 + 0.546060i \(0.183873\pi\)
\(270\) −0.0811559 + 0.249772i −0.00493899 + 0.0152006i
\(271\) 5.13364 3.72981i 0.311846 0.226570i −0.420842 0.907134i \(-0.638265\pi\)
0.732688 + 0.680564i \(0.238265\pi\)
\(272\) 5.59507 + 4.06506i 0.339251 + 0.246480i
\(273\) −4.20285 12.9351i −0.254368 0.782865i
\(274\) 37.9794 2.29442
\(275\) 0 0
\(276\) 43.5443 2.62106
\(277\) −7.41776 22.8295i −0.445690 1.37169i −0.881725 0.471763i \(-0.843618\pi\)
0.436035 0.899930i \(-0.356382\pi\)
\(278\) −5.63707 4.09557i −0.338089 0.245636i
\(279\) −15.4572 + 11.2303i −0.925400 + 0.672342i
\(280\) 0.00101876 0.00313541i 6.08824e−5 0.000187377i
\(281\) −0.992389 + 3.05426i −0.0592009 + 0.182202i −0.976284 0.216495i \(-0.930537\pi\)
0.917083 + 0.398697i \(0.130537\pi\)
\(282\) 40.0790 29.1191i 2.38667 1.73402i
\(283\) 16.8303 + 12.2279i 1.00046 + 0.726875i 0.962186 0.272393i \(-0.0878150\pi\)
0.0382710 + 0.999267i \(0.487815\pi\)
\(284\) 1.22519 + 3.77076i 0.0727018 + 0.223753i
\(285\) −0.103075 −0.00610567
\(286\) 0 0
\(287\) −10.5987 −0.625624
\(288\) −11.6749 35.9317i −0.687951 2.11730i
\(289\) 11.4732 + 8.33579i 0.674896 + 0.490341i
\(290\) −0.276358 + 0.200786i −0.0162283 + 0.0117906i
\(291\) 2.92471 9.00132i 0.171449 0.527667i
\(292\) −6.27079 + 19.2995i −0.366970 + 1.12942i
\(293\) −4.46370 + 3.24307i −0.260772 + 0.189462i −0.710487 0.703710i \(-0.751526\pi\)
0.449715 + 0.893172i \(0.351526\pi\)
\(294\) −4.47357 3.25024i −0.260904 0.189558i
\(295\) −0.0809562 0.249157i −0.00471345 0.0145065i
\(296\) −0.0637988 −0.00370823
\(297\) 0 0
\(298\) −6.20444 −0.359414
\(299\) −12.1610 37.4277i −0.703289 2.16450i
\(300\) 21.8438 + 15.8704i 1.26115 + 0.916280i
\(301\) −3.02547 + 2.19813i −0.174385 + 0.126698i
\(302\) 12.0942 37.2221i 0.695942 2.14189i
\(303\) −3.48581 + 10.7282i −0.200254 + 0.616320i
\(304\) 4.57910 3.32691i 0.262629 0.190811i
\(305\) 0.184435 + 0.134000i 0.0105607 + 0.00767282i
\(306\) 4.90457 + 15.0947i 0.280376 + 0.862908i
\(307\) 8.60991 0.491394 0.245697 0.969347i \(-0.420983\pi\)
0.245697 + 0.969347i \(0.420983\pi\)
\(308\) 0 0
\(309\) −11.0145 −0.626594
\(310\) −0.0662193 0.203802i −0.00376100 0.0115752i
\(311\) −15.4731 11.2419i −0.877400 0.637469i 0.0551620 0.998477i \(-0.482432\pi\)
−0.932562 + 0.361009i \(0.882432\pi\)
\(312\) −1.34730 + 0.978868i −0.0762756 + 0.0554175i
\(313\) −0.187498 + 0.577058i −0.0105980 + 0.0326173i −0.956216 0.292663i \(-0.905459\pi\)
0.945618 + 0.325280i \(0.105459\pi\)
\(314\) −14.0769 + 43.3241i −0.794404 + 2.44492i
\(315\) 0.103770 0.0753936i 0.00584680 0.00424795i
\(316\) −9.18166 6.67087i −0.516509 0.375266i
\(317\) −1.61085 4.95769i −0.0904745 0.278452i 0.895573 0.444914i \(-0.146766\pi\)
−0.986048 + 0.166462i \(0.946766\pi\)
\(318\) −21.9005 −1.22812
\(319\) 0 0
\(320\) 0.201906 0.0112869
\(321\) 8.95364 + 27.5565i 0.499744 + 1.53805i
\(322\) −12.9443 9.40461i −0.721360 0.524098i
\(323\) −1.86603 + 1.35575i −0.103829 + 0.0754361i
\(324\) −0.357209 + 1.09938i −0.0198449 + 0.0610765i
\(325\) 7.54065 23.2077i 0.418280 1.28733i
\(326\) −30.4871 + 22.1502i −1.68852 + 1.22678i
\(327\) 8.51420 + 6.18593i 0.470836 + 0.342083i
\(328\) 0.401033 + 1.23425i 0.0221434 + 0.0681502i
\(329\) −8.95906 −0.493929
\(330\) 0 0
\(331\) 0.669012 0.0367722 0.0183861 0.999831i \(-0.494147\pi\)
0.0183861 + 0.999831i \(0.494147\pi\)
\(332\) 1.56060 + 4.80302i 0.0856488 + 0.263600i
\(333\) −2.00816 1.45901i −0.110046 0.0799533i
\(334\) 4.84933 3.52324i 0.265343 0.192783i
\(335\) −0.0234031 + 0.0720274i −0.00127865 + 0.00393527i
\(336\) −3.54715 + 10.9170i −0.193513 + 0.595571i
\(337\) 5.34125 3.88065i 0.290957 0.211392i −0.432726 0.901526i \(-0.642448\pi\)
0.723682 + 0.690133i \(0.242448\pi\)
\(338\) −17.3801 12.6274i −0.945354 0.686840i
\(339\) 5.46649 + 16.8241i 0.296899 + 0.913761i
\(340\) −0.0876111 −0.00475138
\(341\) 0 0
\(342\) 12.9895 0.702393
\(343\) 0.309017 + 0.951057i 0.0166853 + 0.0513522i
\(344\) 0.370456 + 0.269152i 0.0199736 + 0.0145117i
\(345\) 0.489342 0.355528i 0.0263453 0.0191410i
\(346\) 5.41885 16.6775i 0.291319 0.896587i
\(347\) 3.77005 11.6030i 0.202387 0.622882i −0.797424 0.603420i \(-0.793804\pi\)
0.999811 0.0194628i \(-0.00619560\pi\)
\(348\) 27.9342 20.2954i 1.49743 1.08795i
\(349\) 0.716627 + 0.520660i 0.0383602 + 0.0278703i 0.606800 0.794854i \(-0.292453\pi\)
−0.568440 + 0.822725i \(0.692453\pi\)
\(350\) −3.06580 9.43556i −0.163874 0.504352i
\(351\) −23.9915 −1.28057
\(352\) 0 0
\(353\) 5.36012 0.285291 0.142645 0.989774i \(-0.454439\pi\)
0.142645 + 0.989774i \(0.454439\pi\)
\(354\) 16.6265 + 51.1712i 0.883690 + 2.71972i
\(355\) 0.0445558 + 0.0323717i 0.00236477 + 0.00171811i
\(356\) −1.90983 + 1.38757i −0.101221 + 0.0735413i
\(357\) 1.44550 4.44879i 0.0765040 0.235455i
\(358\) 5.19074 15.9755i 0.274339 0.844330i
\(359\) −20.9090 + 15.1913i −1.10354 + 0.801767i −0.981634 0.190775i \(-0.938900\pi\)
−0.121903 + 0.992542i \(0.538900\pi\)
\(360\) −0.0127062 0.00923162i −0.000669677 0.000486549i
\(361\) −5.28799 16.2748i −0.278315 0.856566i
\(362\) −48.0268 −2.52423
\(363\) 0 0
\(364\) −9.46107 −0.495895
\(365\) 0.0871057 + 0.268084i 0.00455932 + 0.0140321i
\(366\) −37.8787 27.5205i −1.97995 1.43852i
\(367\) 16.5448 12.0205i 0.863629 0.627463i −0.0652408 0.997870i \(-0.520782\pi\)
0.928870 + 0.370406i \(0.120782\pi\)
\(368\) −10.2637 + 31.5885i −0.535033 + 1.64666i
\(369\) −15.6030 + 48.0210i −0.812259 + 2.49987i
\(370\) 0.0225230 0.0163639i 0.00117091 0.000850719i
\(371\) 3.20417 + 2.32797i 0.166352 + 0.120862i
\(372\) 6.69343 + 20.6003i 0.347038 + 1.06807i
\(373\) 9.39109 0.486252 0.243126 0.969995i \(-0.421827\pi\)
0.243126 + 0.969995i \(0.421827\pi\)
\(374\) 0 0
\(375\) 0.750163 0.0387383
\(376\) 0.338991 + 1.04331i 0.0174821 + 0.0538045i
\(377\) −25.2460 18.3423i −1.30024 0.944676i
\(378\) −7.89133 + 5.73339i −0.405886 + 0.294894i
\(379\) −1.74160 + 5.36009i −0.0894599 + 0.275329i −0.985770 0.168098i \(-0.946238\pi\)
0.896310 + 0.443427i \(0.146238\pi\)
\(380\) −0.0221573 + 0.0681931i −0.00113664 + 0.00349823i
\(381\) 11.3417 8.24024i 0.581054 0.422160i
\(382\) 12.5024 + 9.08350i 0.639677 + 0.464752i
\(383\) −0.389189 1.19780i −0.0198866 0.0612047i 0.940621 0.339459i \(-0.110244\pi\)
−0.960507 + 0.278255i \(0.910244\pi\)
\(384\) 2.72816 0.139221
\(385\) 0 0
\(386\) 33.8631 1.72359
\(387\) 5.50539 + 16.9438i 0.279855 + 0.861304i
\(388\) −5.32643 3.86988i −0.270408 0.196463i
\(389\) 4.76033 3.45858i 0.241358 0.175357i −0.460530 0.887644i \(-0.652341\pi\)
0.701888 + 0.712287i \(0.252341\pi\)
\(390\) 0.224566 0.691142i 0.0113713 0.0349974i
\(391\) 4.18257 12.8726i 0.211522 0.650997i
\(392\) 0.0990607 0.0719718i 0.00500332 0.00363512i
\(393\) 8.48400 + 6.16399i 0.427961 + 0.310932i
\(394\) −3.71344 11.4288i −0.187080 0.575774i
\(395\) −0.157648 −0.00793212
\(396\) 0 0
\(397\) 4.86018 0.243925 0.121963 0.992535i \(-0.461081\pi\)
0.121963 + 0.992535i \(0.461081\pi\)
\(398\) −8.41261 25.8914i −0.421686 1.29782i
\(399\) −3.09719 2.25024i −0.155054 0.112653i
\(400\) −16.6617 + 12.1054i −0.833085 + 0.605271i
\(401\) −7.88987 + 24.2825i −0.394001 + 1.21261i 0.535735 + 0.844386i \(0.320035\pi\)
−0.929736 + 0.368226i \(0.879965\pi\)
\(402\) 4.80646 14.7928i 0.239724 0.737796i
\(403\) 15.8373 11.5064i 0.788910 0.573177i
\(404\) 6.34830 + 4.61231i 0.315839 + 0.229471i
\(405\) 0.00496188 + 0.0152711i 0.000246558 + 0.000758827i
\(406\) −12.6873 −0.629661
\(407\) 0 0
\(408\) −0.572769 −0.0283563
\(409\) 6.49760 + 19.9975i 0.321285 + 0.988815i 0.973090 + 0.230427i \(0.0740124\pi\)
−0.651804 + 0.758387i \(0.725988\pi\)
\(410\) −0.458154 0.332868i −0.0226266 0.0164392i
\(411\) −43.1413 + 31.3440i −2.12801 + 1.54609i
\(412\) −2.36770 + 7.28703i −0.116648 + 0.359006i
\(413\) 3.00680 9.25399i 0.147955 0.455359i
\(414\) −61.6667 + 44.8035i −3.03075 + 2.20197i
\(415\) 0.0567531 + 0.0412335i 0.00278590 + 0.00202408i
\(416\) 11.9620 + 36.8151i 0.586484 + 1.80501i
\(417\) 9.78326 0.479088
\(418\) 0 0
\(419\) −31.3141 −1.52980 −0.764898 0.644151i \(-0.777211\pi\)
−0.764898 + 0.644151i \(0.777211\pi\)
\(420\) −0.0449356 0.138298i −0.00219263 0.00674823i
\(421\) −10.3462 7.51698i −0.504244 0.366355i 0.306391 0.951906i \(-0.400878\pi\)
−0.810636 + 0.585551i \(0.800878\pi\)
\(422\) −28.9557 + 21.0376i −1.40954 + 1.02409i
\(423\) −13.1891 + 40.5919i −0.641277 + 1.97365i
\(424\) 0.149859 0.461220i 0.00727782 0.0223988i
\(425\) 6.78982 4.93309i 0.329355 0.239290i
\(426\) −9.15073 6.64839i −0.443354 0.322116i
\(427\) 2.61652 + 8.05281i 0.126622 + 0.389703i
\(428\) 20.1556 0.974258
\(429\) 0 0
\(430\) −0.199818 −0.00963607
\(431\) 6.51033 + 20.0367i 0.313592 + 0.965136i 0.976330 + 0.216285i \(0.0693941\pi\)
−0.662738 + 0.748851i \(0.730606\pi\)
\(432\) 16.3814 + 11.9018i 0.788149 + 0.572624i
\(433\) −30.7451 + 22.3376i −1.47752 + 1.07348i −0.499169 + 0.866505i \(0.666361\pi\)
−0.978347 + 0.206973i \(0.933639\pi\)
\(434\) 2.45946 7.56944i 0.118058 0.363345i
\(435\) 0.148213 0.456152i 0.00710625 0.0218708i
\(436\) 5.92273 4.30312i 0.283647 0.206082i
\(437\) −8.96176 6.51110i −0.428699 0.311468i
\(438\) −17.8895 55.0582i −0.854793 2.63078i
\(439\) −37.7677 −1.80256 −0.901278 0.433241i \(-0.857370\pi\)
−0.901278 + 0.433241i \(0.857370\pi\)
\(440\) 0 0
\(441\) 4.76399 0.226857
\(442\) −5.02516 15.4658i −0.239022 0.735635i
\(443\) 0.831607 + 0.604198i 0.0395108 + 0.0287063i 0.607365 0.794423i \(-0.292226\pi\)
−0.567855 + 0.823129i \(0.692226\pi\)
\(444\) −2.27662 + 1.65406i −0.108044 + 0.0784982i
\(445\) −0.0101331 + 0.0311866i −0.000480357 + 0.00147839i
\(446\) −4.00644 + 12.3306i −0.189710 + 0.583869i
\(447\) 7.04772 5.12047i 0.333346 0.242190i
\(448\) 6.06683 + 4.40781i 0.286631 + 0.208250i
\(449\) 6.22153 + 19.1479i 0.293612 + 0.903645i 0.983684 + 0.179904i \(0.0575789\pi\)
−0.690072 + 0.723741i \(0.742421\pi\)
\(450\) −47.2642 −2.22806
\(451\) 0 0
\(452\) 12.3057 0.578809
\(453\) 16.9810 + 52.2623i 0.797839 + 2.45550i
\(454\) −21.8473 15.8730i −1.02534 0.744955i
\(455\) −0.106322 + 0.0772472i −0.00498444 + 0.00362141i
\(456\) −0.144856 + 0.445821i −0.00678350 + 0.0208775i
\(457\) −7.46140 + 22.9638i −0.349030 + 1.07420i 0.610362 + 0.792123i \(0.291024\pi\)
−0.959391 + 0.282079i \(0.908976\pi\)
\(458\) 31.1807 22.6541i 1.45698 1.05856i
\(459\) −6.67559 4.85010i −0.311590 0.226383i
\(460\) −0.130022 0.400166i −0.00606229 0.0186578i
\(461\) 11.5885 0.539731 0.269865 0.962898i \(-0.413021\pi\)
0.269865 + 0.962898i \(0.413021\pi\)
\(462\) 0 0
\(463\) 21.6077 1.00419 0.502097 0.864811i \(-0.332562\pi\)
0.502097 + 0.864811i \(0.332562\pi\)
\(464\) 8.13865 + 25.0482i 0.377827 + 1.16283i
\(465\) 0.243415 + 0.176852i 0.0112881 + 0.00820130i
\(466\) −7.00242 + 5.08756i −0.324381 + 0.235676i
\(467\) 4.91799 15.1360i 0.227577 0.700411i −0.770442 0.637510i \(-0.779965\pi\)
0.998020 0.0629015i \(-0.0200354\pi\)
\(468\) −13.9281 + 42.8664i −0.643829 + 1.98150i
\(469\) −2.27564 + 1.65335i −0.105079 + 0.0763446i
\(470\) −0.387275 0.281372i −0.0178637 0.0129787i
\(471\) −19.7649 60.8300i −0.910717 2.80290i
\(472\) −1.19142 −0.0548397
\(473\) 0 0
\(474\) 32.3772 1.48713
\(475\) −2.12255 6.53253i −0.0973892 0.299733i
\(476\) −2.63252 1.91264i −0.120661 0.0876657i
\(477\) 15.2646 11.0904i 0.698920 0.507795i
\(478\) 6.49438 19.9876i 0.297046 0.914213i
\(479\) 1.63276 5.02511i 0.0746026 0.229603i −0.906801 0.421559i \(-0.861483\pi\)
0.981404 + 0.191956i \(0.0614830\pi\)
\(480\) −0.481333 + 0.349709i −0.0219698 + 0.0159620i
\(481\) 2.05753 + 1.49488i 0.0938153 + 0.0681608i
\(482\) 11.4608 + 35.2727i 0.522025 + 1.60663i
\(483\) 22.4652 1.02220
\(484\) 0 0
\(485\) −0.0914540 −0.00415271
\(486\) −10.0617 30.9668i −0.456409 1.40468i
\(487\) 21.8965 + 15.9087i 0.992225 + 0.720894i 0.960407 0.278600i \(-0.0898704\pi\)
0.0318177 + 0.999494i \(0.489870\pi\)
\(488\) 0.838769 0.609401i 0.0379693 0.0275863i
\(489\) 16.3504 50.3214i 0.739391 2.27561i
\(490\) −0.0165113 + 0.0508166i −0.000745905 + 0.00229566i
\(491\) −15.2095 + 11.0503i −0.686395 + 0.498695i −0.875473 0.483267i \(-0.839450\pi\)
0.189078 + 0.981962i \(0.439450\pi\)
\(492\) 46.3101 + 33.6462i 2.08782 + 1.51689i
\(493\) −3.31659 10.2074i −0.149372 0.459719i
\(494\) −13.3089 −0.598795
\(495\) 0 0
\(496\) −16.5218 −0.741851
\(497\) 0.632097 + 1.94539i 0.0283534 + 0.0872629i
\(498\) −11.6558 8.46842i −0.522308 0.379479i
\(499\) 32.1719 23.3743i 1.44021 1.04638i 0.452214 0.891909i \(-0.350634\pi\)
0.987998 0.154466i \(-0.0493657\pi\)
\(500\) 0.161256 0.496296i 0.00721160 0.0221950i
\(501\) −2.60072 + 8.00421i −0.116192 + 0.357602i
\(502\) −30.4776 + 22.1433i −1.36028 + 0.988302i
\(503\) −32.8157 23.8420i −1.46318 1.06306i −0.982521 0.186154i \(-0.940398\pi\)
−0.480658 0.876908i \(-0.659602\pi\)
\(504\) −0.180259 0.554780i −0.00802937 0.0247119i
\(505\) 0.108999 0.00485040
\(506\) 0 0
\(507\) 30.1636 1.33961
\(508\) −3.01357 9.27483i −0.133706 0.411504i
\(509\) 12.5243 + 9.09945i 0.555131 + 0.403326i 0.829674 0.558249i \(-0.188527\pi\)
−0.274543 + 0.961575i \(0.588527\pi\)
\(510\) 0.202206 0.146911i 0.00895381 0.00650532i
\(511\) −3.23520 + 9.95693i −0.143117 + 0.440469i
\(512\) 9.78397 30.1120i 0.432395 1.33077i
\(513\) −5.46341 + 3.96940i −0.241216 + 0.175253i
\(514\) 22.0100 + 15.9912i 0.970817 + 0.705340i
\(515\) 0.0328890 + 0.101222i 0.00144926 + 0.00446037i
\(516\) 20.1975 0.889147
\(517\) 0 0
\(518\) 1.03401 0.0454317
\(519\) 7.60843 + 23.4163i 0.333973 + 1.02786i
\(520\) 0.0130186 + 0.00945859i 0.000570905 + 0.000414787i
\(521\) −30.3169 + 22.0265i −1.32821 + 0.965000i −0.328418 + 0.944532i \(0.606516\pi\)
−0.999791 + 0.0204678i \(0.993484\pi\)
\(522\) −18.6777 + 57.4840i −0.817500 + 2.51601i
\(523\) −6.43111 + 19.7929i −0.281213 + 0.865484i 0.706295 + 0.707917i \(0.250365\pi\)
−0.987508 + 0.157567i \(0.949635\pi\)
\(524\) 5.90172 4.28785i 0.257818 0.187316i
\(525\) 11.2696 + 8.18782i 0.491844 + 0.357346i
\(526\) 10.1657 + 31.2867i 0.443244 + 1.36417i
\(527\) 6.73281 0.293286
\(528\) 0 0
\(529\) 42.0033 1.82623
\(530\) 0.0653943 + 0.201263i 0.00284055 + 0.00874230i
\(531\) −37.5017 27.2466i −1.62744 1.18240i
\(532\) −2.15450 + 1.56534i −0.0934094 + 0.0678659i
\(533\) 15.9866 49.2017i 0.692456 2.13116i
\(534\) 2.08111 6.40501i 0.0900586 0.277172i
\(535\) 0.226505 0.164565i 0.00979266 0.00711478i
\(536\) 0.278643 + 0.202446i 0.0120355 + 0.00874432i
\(537\) 7.28816 + 22.4306i 0.314507 + 0.967954i
\(538\) −16.9549 −0.730979
\(539\) 0 0
\(540\) −0.256510 −0.0110384
\(541\) −5.38488 16.5730i −0.231514 0.712528i −0.997565 0.0697472i \(-0.977781\pi\)
0.766050 0.642780i \(-0.222219\pi\)
\(542\) 10.1878 + 7.40186i 0.437603 + 0.317937i
\(543\) 54.5544 39.6361i 2.34115 1.70095i
\(544\) −4.11412 + 12.6620i −0.176391 + 0.542877i
\(545\) 0.0314247 0.0967152i 0.00134609 0.00414283i
\(546\) 21.8360 15.8648i 0.934496 0.678951i
\(547\) 12.7792 + 9.28463i 0.546399 + 0.396982i 0.826456 0.563001i \(-0.190353\pi\)
−0.280057 + 0.959983i \(0.590353\pi\)
\(548\) 11.4630 + 35.2794i 0.489673 + 1.50706i
\(549\) 40.3378 1.72157
\(550\) 0 0
\(551\) −8.78382 −0.374203
\(552\) −0.850034 2.61613i −0.0361798 0.111350i
\(553\) −4.73697 3.44161i −0.201436 0.146352i
\(554\) 38.5392 28.0004i 1.63737 1.18962i
\(555\) −0.0120792 + 0.0371760i −0.000512734 + 0.00157803i
\(556\) 2.10303 6.47245i 0.0891881 0.274493i
\(557\) 13.6199 9.89541i 0.577092 0.419282i −0.260582 0.965452i \(-0.583915\pi\)
0.837675 + 0.546170i \(0.183915\pi\)
\(558\) −30.6751 22.2868i −1.29858 0.943474i
\(559\) −5.64075 17.3604i −0.238578 0.734268i
\(560\) 0.110917 0.00468711
\(561\) 0 0
\(562\) −6.37315 −0.268835
\(563\) −11.5666 35.5984i −0.487475 1.50029i −0.828364 0.560190i \(-0.810728\pi\)
0.340889 0.940104i \(-0.389272\pi\)
\(564\) 39.1457 + 28.4410i 1.64833 + 1.19758i
\(565\) 0.138289 0.100473i 0.00581785 0.00422691i
\(566\) −12.7577 + 39.2640i −0.536244 + 1.65039i
\(567\) −0.184290 + 0.567186i −0.00773945 + 0.0238196i
\(568\) 0.202629 0.147219i 0.00850214 0.00617717i
\(569\) 2.24025 + 1.62763i 0.0939160 + 0.0682340i 0.633752 0.773536i \(-0.281514\pi\)
−0.539836 + 0.841770i \(0.681514\pi\)
\(570\) −0.0632109 0.194543i −0.00264761 0.00814852i
\(571\) −8.85289 −0.370482 −0.185241 0.982693i \(-0.559307\pi\)
−0.185241 + 0.982693i \(0.559307\pi\)
\(572\) 0 0
\(573\) −21.6981 −0.906453
\(574\) −6.49967 20.0039i −0.271291 0.834947i
\(575\) 32.6086 + 23.6916i 1.35987 + 0.988006i
\(576\) 28.9023 20.9988i 1.20426 0.874949i
\(577\) 11.4856 35.3491i 0.478152 1.47160i −0.363506 0.931592i \(-0.618420\pi\)
0.841659 0.540010i \(-0.181580\pi\)
\(578\) −8.69691 + 26.7663i −0.361744 + 1.11333i
\(579\) −38.4656 + 27.9469i −1.59857 + 1.16143i
\(580\) −0.269922 0.196110i −0.0112079 0.00814303i
\(581\) 0.805136 + 2.47795i 0.0334027 + 0.102803i
\(582\) 18.7825 0.778562
\(583\) 0 0
\(584\) 1.28193 0.0530464
\(585\) 0.193472 + 0.595445i 0.00799907 + 0.0246186i
\(586\) −8.85829 6.43592i −0.365933 0.265866i
\(587\) 28.5736 20.7599i 1.17936 0.856854i 0.187259 0.982311i \(-0.440040\pi\)
0.992099 + 0.125457i \(0.0400396\pi\)
\(588\) 1.66896 5.13653i 0.0688267 0.211827i
\(589\) 1.70276 5.24056i 0.0701610 0.215933i
\(590\) 0.420610 0.305591i 0.0173162 0.0125810i
\(591\) 13.6502 + 9.91747i 0.561495 + 0.407950i
\(592\) −0.663294 2.04141i −0.0272612 0.0839014i
\(593\) −8.09224 −0.332308 −0.166154 0.986100i \(-0.553135\pi\)
−0.166154 + 0.986100i \(0.553135\pi\)
\(594\) 0 0
\(595\) −0.0452000 −0.00185302
\(596\) −1.87263 5.76336i −0.0767058 0.236076i
\(597\) 30.9239 + 22.4675i 1.26563 + 0.919535i
\(598\) 63.1828 45.9050i 2.58374 1.87720i
\(599\) 1.18544 3.64841i 0.0484357 0.149070i −0.923913 0.382601i \(-0.875028\pi\)
0.972349 + 0.233532i \(0.0750282\pi\)
\(600\) 0.527079 1.62218i 0.0215179 0.0662253i
\(601\) 11.5986 8.42687i 0.473116 0.343739i −0.325538 0.945529i \(-0.605545\pi\)
0.798655 + 0.601790i \(0.205545\pi\)
\(602\) −6.00409 4.36222i −0.244708 0.177791i
\(603\) 4.14094 + 12.7445i 0.168632 + 0.518997i
\(604\) 38.2261 1.55540
\(605\) 0 0
\(606\) −22.3859 −0.909367
\(607\) 4.25781 + 13.1042i 0.172819 + 0.531883i 0.999527 0.0307486i \(-0.00978911\pi\)
−0.826708 + 0.562631i \(0.809789\pi\)
\(608\) 8.81508 + 6.40453i 0.357499 + 0.259738i
\(609\) 14.4117 10.4707i 0.583992 0.424295i
\(610\) −0.139805 + 0.430276i −0.00566054 + 0.0174214i
\(611\) 13.5134 41.5899i 0.546693 1.68255i
\(612\) −12.5413 + 9.11179i −0.506952 + 0.368322i
\(613\) 7.72154 + 5.61003i 0.311870 + 0.226587i 0.732699 0.680553i \(-0.238261\pi\)
−0.420828 + 0.907140i \(0.638261\pi\)
\(614\) 5.28002 + 16.2502i 0.213084 + 0.655806i
\(615\) 0.795137 0.0320630
\(616\) 0 0
\(617\) −31.5153 −1.26876 −0.634379 0.773023i \(-0.718744\pi\)
−0.634379 + 0.773023i \(0.718744\pi\)
\(618\) −6.75464 20.7887i −0.271712 0.836243i
\(619\) −16.6089 12.0671i −0.667568 0.485016i 0.201642 0.979459i \(-0.435372\pi\)
−0.869210 + 0.494443i \(0.835372\pi\)
\(620\) 0.169327 0.123023i 0.00680034 0.00494074i
\(621\) 12.2458 37.6888i 0.491409 1.51240i
\(622\) 11.7289 36.0978i 0.470286 1.44739i
\(623\) −0.985313 + 0.715872i −0.0394757 + 0.0286808i
\(624\) −45.3288 32.9333i −1.81460 1.31839i
\(625\) 7.72206 + 23.7661i 0.308883 + 0.950643i
\(626\) −1.20411 −0.0481261
\(627\) 0 0
\(628\) −44.4928 −1.77546
\(629\) 0.270299 + 0.831896i 0.0107775 + 0.0331699i
\(630\) 0.205934 + 0.149620i 0.00820460 + 0.00596099i
\(631\) −29.0970 + 21.1402i −1.15833 + 0.841578i −0.989566 0.144078i \(-0.953978\pi\)
−0.168766 + 0.985656i \(0.553978\pi\)
\(632\) −0.221548 + 0.681856i −0.00881272 + 0.0271228i
\(633\) 15.5291 47.7937i 0.617227 1.89963i
\(634\) 8.36923 6.08060i 0.332384 0.241491i
\(635\) −0.109593 0.0796237i −0.00434905 0.00315977i
\(636\) −6.61004 20.3436i −0.262105 0.806676i
\(637\) −4.88112 −0.193397
\(638\) 0 0
\(639\) 9.74478 0.385498
\(640\) −0.00814618 0.0250714i −0.000322006 0.000991033i
\(641\) −11.0192 8.00590i −0.435232 0.316214i 0.348506 0.937307i \(-0.386689\pi\)
−0.783737 + 0.621092i \(0.786689\pi\)
\(642\) −46.5189 + 33.7980i −1.83595 + 1.33390i
\(643\) 6.79501 20.9129i 0.267969 0.824724i −0.723026 0.690821i \(-0.757249\pi\)
0.990995 0.133902i \(-0.0427509\pi\)
\(644\) 4.82915 14.8626i 0.190295 0.585669i
\(645\) 0.226976 0.164908i 0.00893717 0.00649323i
\(646\) −3.70317 2.69051i −0.145699 0.105857i
\(647\) −4.57971 14.0949i −0.180047 0.554128i 0.819781 0.572677i \(-0.194095\pi\)
−0.999828 + 0.0185496i \(0.994095\pi\)
\(648\) 0.0730235 0.00286863
\(649\) 0 0
\(650\) 48.4262 1.89943
\(651\) 3.45325 + 10.6280i 0.135343 + 0.416544i
\(652\) −29.7771 21.6343i −1.16616 0.847266i
\(653\) −35.0932 + 25.4967i −1.37330 + 0.997763i −0.375832 + 0.926688i \(0.622643\pi\)
−0.997471 + 0.0710750i \(0.977357\pi\)
\(654\) −6.45391 + 19.8631i −0.252368 + 0.776708i
\(655\) 0.0313132 0.0963722i 0.00122351 0.00376557i
\(656\) −35.3237 + 25.6642i −1.37916 + 1.00202i
\(657\) 40.3504 + 29.3163i 1.57422 + 1.14374i
\(658\) −5.49414 16.9092i −0.214184 0.659190i
\(659\) 42.2093 1.64424 0.822121 0.569313i \(-0.192791\pi\)
0.822121 + 0.569313i \(0.192791\pi\)
\(660\) 0 0
\(661\) 16.2794 0.633197 0.316599 0.948560i \(-0.397459\pi\)
0.316599 + 0.948560i \(0.397459\pi\)
\(662\) 0.410271 + 1.26268i 0.0159456 + 0.0490756i
\(663\) 18.4720 + 13.4207i 0.717392 + 0.521215i
\(664\) 0.258100 0.187521i 0.0100162 0.00727722i
\(665\) −0.0114313 + 0.0351819i −0.000443286 + 0.00136430i
\(666\) 1.52222 4.68490i 0.0589847 0.181536i
\(667\) 41.7005 30.2972i 1.61465 1.17311i
\(668\) 4.73640 + 3.44119i 0.183257 + 0.133144i
\(669\) −5.62531 17.3129i −0.217487 0.669357i
\(670\) −0.150295 −0.00580642
\(671\) 0 0
\(672\) −22.0975 −0.852430
\(673\) −1.64103 5.05056i −0.0632569 0.194685i 0.914433 0.404736i \(-0.132637\pi\)
−0.977690 + 0.210052i \(0.932637\pi\)
\(674\) 10.5998 + 7.70120i 0.408289 + 0.296639i
\(675\) 19.8794 14.4432i 0.765158 0.555920i
\(676\) 6.48401 19.9557i 0.249385 0.767529i
\(677\) −10.4431 + 32.1407i −0.401363 + 1.23527i 0.522532 + 0.852620i \(0.324988\pi\)
−0.923894 + 0.382648i \(0.875012\pi\)
\(678\) −28.4013 + 20.6348i −1.09075 + 0.792473i
\(679\) −2.74799 1.99653i −0.105458 0.0766199i
\(680\) 0.00171027 + 0.00526367i 6.55858e−5 + 0.000201852i
\(681\) 37.9164 1.45296
\(682\) 0 0
\(683\) −15.8834 −0.607761 −0.303880 0.952710i \(-0.598282\pi\)
−0.303880 + 0.952710i \(0.598282\pi\)
\(684\) 3.92050 + 12.0661i 0.149904 + 0.461358i
\(685\) 0.416866 + 0.302871i 0.0159276 + 0.0115721i
\(686\) −1.60551 + 1.16647i −0.0612985 + 0.0445360i
\(687\) −16.7224 + 51.4662i −0.637999 + 1.96356i
\(688\) −4.76071 + 14.6520i −0.181500 + 0.558601i
\(689\) −15.6399 + 11.3631i −0.595834 + 0.432899i
\(690\) 0.971107 + 0.705551i 0.0369694 + 0.0268599i
\(691\) 7.89151 + 24.2876i 0.300207 + 0.923942i 0.981422 + 0.191859i \(0.0614517\pi\)
−0.681215 + 0.732083i \(0.738548\pi\)
\(692\) 17.1274 0.651085
\(693\) 0 0
\(694\) 24.2113 0.919050
\(695\) −0.0292125 0.0899068i −0.00110809 0.00341036i
\(696\) −1.76465 1.28210i −0.0668890 0.0485977i
\(697\) 14.3948 10.4584i 0.545242 0.396141i
\(698\) −0.543216 + 1.67185i −0.0205610 + 0.0632803i
\(699\) 3.75544 11.5581i 0.142044 0.437166i
\(700\) 7.83945 5.69569i 0.296303 0.215277i
\(701\) 2.66600 + 1.93696i 0.100693 + 0.0731579i 0.636993 0.770870i \(-0.280178\pi\)
−0.536299 + 0.844028i \(0.680178\pi\)
\(702\) −14.7128 45.2813i −0.555298 1.70903i
\(703\) 0.715875 0.0269997
\(704\) 0 0
\(705\) 0.672125 0.0253137
\(706\) 3.28709 + 10.1166i 0.123711 + 0.380744i
\(707\) 3.27519 + 2.37956i 0.123176 + 0.0894927i
\(708\) −42.5151 + 30.8891i −1.59782 + 1.16088i
\(709\) −13.8757 + 42.7049i −0.521111 + 1.60382i 0.250768 + 0.968047i \(0.419317\pi\)
−0.771880 + 0.635769i \(0.780683\pi\)
\(710\) −0.0337740 + 0.103946i −0.00126752 + 0.00390102i
\(711\) −22.5669 + 16.3958i −0.846323 + 0.614890i
\(712\) 0.120647 + 0.0876554i 0.00452145 + 0.00328503i
\(713\) 9.99202 + 30.7523i 0.374204 + 1.15168i
\(714\) 9.28304 0.347409
\(715\) 0 0
\(716\) 16.4064 0.613137
\(717\) 9.11855 + 28.0640i 0.340538 + 1.04807i
\(718\) −41.4943 30.1474i −1.54855 1.12509i
\(719\) −2.58290 + 1.87659i −0.0963259 + 0.0699849i −0.634906 0.772590i \(-0.718961\pi\)
0.538580 + 0.842575i \(0.318961\pi\)
\(720\) 0.163287 0.502547i 0.00608536 0.0187288i
\(721\) −1.22153 + 3.75950i −0.0454923 + 0.140011i
\(722\) 27.4739 19.9609i 1.02247 0.742869i
\(723\) −42.1287 30.6083i −1.56678 1.13834i
\(724\) −14.4955 44.6125i −0.538721 1.65801i
\(725\) 31.9612 1.18701
\(726\) 0 0
\(727\) 20.1654 0.747891 0.373946 0.927451i \(-0.378005\pi\)
0.373946 + 0.927451i \(0.378005\pi\)
\(728\) 0.184691 + 0.568420i 0.00684510 + 0.0210670i
\(729\) 35.5384 + 25.8202i 1.31624 + 0.956303i
\(730\) −0.452560 + 0.328804i −0.0167500 + 0.0121696i
\(731\) 1.94004 5.97083i 0.0717550 0.220839i
\(732\) 14.1315 43.4921i 0.522314 1.60752i
\(733\) 15.9453 11.5849i 0.588952 0.427899i −0.252988 0.967469i \(-0.581413\pi\)
0.841940 + 0.539571i \(0.181413\pi\)
\(734\) 32.8333 + 23.8548i 1.21190 + 0.880496i
\(735\) −0.0231830 0.0713500i −0.000855118 0.00263178i
\(736\) −63.9394 −2.35684
\(737\) 0 0
\(738\) −100.203 −3.68851
\(739\) −10.6789 32.8662i −0.392829 1.20900i −0.930640 0.365937i \(-0.880749\pi\)
0.537811 0.843065i \(-0.319251\pi\)
\(740\) 0.0219985 + 0.0159828i 0.000808680 + 0.000587541i
\(741\) 15.1178 10.9837i 0.555365 0.403496i
\(742\) −2.42882 + 7.47513i −0.0891647 + 0.274421i
\(743\) −7.98443 + 24.5735i −0.292920 + 0.901516i 0.690992 + 0.722862i \(0.257174\pi\)
−0.983912 + 0.178653i \(0.942826\pi\)
\(744\) 1.10700 0.804281i 0.0405845 0.0294864i
\(745\) −0.0681006 0.0494780i −0.00249501 0.00181273i
\(746\) 5.75907 + 17.7246i 0.210855 + 0.648944i
\(747\) 12.4125 0.454148
\(748\) 0 0
\(749\) 10.3986 0.379957
\(750\) 0.460037 + 1.41585i 0.0167982 + 0.0516995i
\(751\) 28.8980 + 20.9956i 1.05450 + 0.766142i 0.973064 0.230536i \(-0.0740480\pi\)
0.0814404 + 0.996678i \(0.474048\pi\)
\(752\) −29.8590 + 21.6938i −1.08884 + 0.791092i
\(753\) 16.3453 50.3057i 0.595656 1.83324i
\(754\) 19.1369 58.8973i 0.696925 2.14491i
\(755\) 0.429578 0.312107i 0.0156340 0.0113587i
\(756\) −7.70756 5.59987i −0.280321 0.203665i
\(757\) −4.57952 14.0943i −0.166446 0.512267i 0.832694 0.553733i \(-0.186797\pi\)
−0.999140 + 0.0414660i \(0.986797\pi\)
\(758\) −11.1846 −0.406242
\(759\) 0 0
\(760\) 0.00452957 0.000164305
\(761\) −6.72913 20.7101i −0.243931 0.750742i −0.995810 0.0914417i \(-0.970852\pi\)
0.751879 0.659301i \(-0.229148\pi\)
\(762\) 22.5078 + 16.3529i 0.815372 + 0.592402i
\(763\) 3.05563 2.22005i 0.110621 0.0803711i
\(764\) −4.66427 + 14.3551i −0.168747 + 0.519351i
\(765\) −0.0665414 + 0.204793i −0.00240581 + 0.00740431i
\(766\) 2.02204 1.46910i 0.0730593 0.0530807i
\(767\) 38.4237 + 27.9165i 1.38740 + 1.00801i
\(768\) 14.5870 + 44.8941i 0.526363 + 1.61998i
\(769\) −35.6991 −1.28734 −0.643672 0.765302i \(-0.722590\pi\)
−0.643672 + 0.765302i \(0.722590\pi\)
\(770\) 0 0
\(771\) −38.1988 −1.37570
\(772\) 10.2206 + 31.4557i 0.367847 + 1.13212i
\(773\) −34.4827 25.0531i −1.24026 0.901098i −0.242640 0.970116i \(-0.578013\pi\)
−0.997615 + 0.0690182i \(0.978013\pi\)
\(774\) −28.6034 + 20.7816i −1.02813 + 0.746979i
\(775\) −6.19573 + 19.0685i −0.222557 + 0.684961i
\(776\) −0.128524 + 0.395556i −0.00461374 + 0.0141996i
\(777\) −1.17454 + 0.853356i −0.0421365 + 0.0306140i
\(778\) 9.44694 + 6.86361i 0.338689 + 0.246072i
\(779\) −4.49992 13.8493i −0.161226 0.496204i
\(780\) 0.709786 0.0254144
\(781\) 0 0
\(782\) 26.8606 0.960533
\(783\) −9.71038 29.8855i −0.347021 1.06802i
\(784\) 3.33282 + 2.42144i 0.119029 + 0.0864799i
\(785\) −0.500002 + 0.363273i −0.0178458 + 0.0129658i
\(786\) −6.43102 + 19.7926i −0.229387 + 0.705980i
\(787\) −14.5506 + 44.7821i −0.518672 + 1.59631i 0.257827 + 0.966191i \(0.416994\pi\)
−0.776499 + 0.630118i \(0.783006\pi\)
\(788\) 9.49551 6.89889i 0.338263 0.245763i
\(789\) −37.3680 27.1494i −1.33033 0.966545i
\(790\) −0.0966773 0.297542i −0.00343962 0.0105861i
\(791\) 6.34869 0.225733
\(792\) 0 0
\(793\) −41.3295 −1.46765
\(794\) 2.98050 + 9.17303i 0.105774 + 0.325538i
\(795\) −0.240383 0.174648i −0.00852550 0.00619414i
\(796\) 21.5116 15.6291i 0.762459 0.553959i
\(797\) −2.31226 + 7.11641i −0.0819045 + 0.252076i −0.983620 0.180253i \(-0.942308\pi\)
0.901716 + 0.432329i \(0.142308\pi\)
\(798\) 2.34772 7.22555i 0.0831086 0.255782i
\(799\) 12.1679 8.84046i 0.430468 0.312753i
\(800\) −32.0749 23.3038i −1.13402 0.823913i
\(801\) 1.79296 + 5.51815i 0.0633510 + 0.194974i
\(802\) −50.6690 −1.78918
\(803\) 0 0
\(804\) 15.1918 0.535774
\(805\) −0.0670803 0.206452i −0.00236427 0.00727648i
\(806\) 31.4293 + 22.8347i 1.10705 + 0.804318i
\(807\) 19.2593 13.9927i 0.677961 0.492568i
\(808\) 0.153181 0.471442i 0.00538888 0.0165853i
\(809\) 10.7380 33.0483i 0.377529 1.16191i −0.564228 0.825619i \(-0.690826\pi\)
0.941757 0.336295i \(-0.109174\pi\)
\(810\) −0.0257796 + 0.0187300i −0.000905803 + 0.000658104i
\(811\) −10.3662 7.53146i −0.364005 0.264465i 0.390715 0.920511i \(-0.372228\pi\)
−0.754721 + 0.656046i \(0.772228\pi\)
\(812\) −3.82930 11.7854i −0.134382 0.413585i
\(813\) −17.6811 −0.620105
\(814\) 0 0
\(815\) −0.511268 −0.0179089
\(816\) −5.95488 18.3272i −0.208462 0.641581i
\(817\) −4.15681 3.02010i −0.145428 0.105660i
\(818\) −33.7584 + 24.5269i −1.18034 + 0.857564i
\(819\) −7.18576 + 22.1155i −0.251091 + 0.772778i
\(820\) 0.170924 0.526049i 0.00596892 0.0183704i
\(821\) 43.9478 31.9300i 1.53379 1.11436i 0.579705 0.814826i \(-0.303168\pi\)
0.954085 0.299538i \(-0.0968324\pi\)
\(822\) −85.6146 62.2027i −2.98615 2.16957i
\(823\) −6.10918 18.8021i −0.212953 0.655401i −0.999293 0.0376067i \(-0.988027\pi\)
0.786340 0.617794i \(-0.211973\pi\)
\(824\) 0.484024 0.0168618
\(825\) 0 0
\(826\) 19.3098 0.671873
\(827\) 3.80395 + 11.7074i 0.132276 + 0.407105i 0.995156 0.0983040i \(-0.0313418\pi\)
−0.862880 + 0.505409i \(0.831342\pi\)
\(828\) −60.2306 43.7601i −2.09316 1.52077i
\(829\) 20.8127 15.1213i 0.722854 0.525184i −0.164441 0.986387i \(-0.552582\pi\)
0.887295 + 0.461203i \(0.152582\pi\)
\(830\) −0.0430198 + 0.132401i −0.00149324 + 0.00459572i
\(831\) −20.6688 + 63.6120i −0.716993 + 2.20668i
\(832\) −29.6129 + 21.5151i −1.02664 + 0.745900i
\(833\) −1.35816 0.986762i −0.0470575 0.0341893i
\(834\) 5.99957 + 18.4648i 0.207748 + 0.639383i
\(835\) 0.0813232 0.00281431
\(836\) 0 0
\(837\) 19.7125 0.681363
\(838\) −19.2034 59.1019i −0.663369 2.04164i
\(839\) 37.7112 + 27.3988i 1.30194 + 0.945912i 0.999973 0.00740804i \(-0.00235807\pi\)
0.301963 + 0.953320i \(0.402358\pi\)
\(840\) −0.00743171 + 0.00539945i −0.000256418 + 0.000186299i
\(841\) 3.66881 11.2914i 0.126511 0.389359i
\(842\) 7.84262 24.1371i 0.270275 0.831820i
\(843\) 7.23935 5.25970i 0.249336 0.181154i
\(844\) −28.2814 20.5476i −0.973485 0.707279i
\(845\) −0.0900675 0.277199i −0.00309842 0.00953594i
\(846\) −84.7009 −2.91208
\(847\) 0 0
\(848\) 16.3160 0.560292
\(849\) −17.9126 55.1293i −0.614759 1.89203i
\(850\) 13.4745 + 9.78980i 0.462171 + 0.335787i
\(851\) −3.39856 + 2.46920i −0.116501 + 0.0846430i
\(852\) 3.41387 10.5068i 0.116957 0.359957i
\(853\) −3.03109 + 9.32873i −0.103782 + 0.319410i −0.989443 0.144924i \(-0.953706\pi\)
0.885660 + 0.464334i \(0.153706\pi\)
\(854\) −13.5942 + 9.87675i −0.465183 + 0.337976i
\(855\) 0.142574 + 0.103586i 0.00487594 + 0.00354258i
\(856\) −0.393460 1.21095i −0.0134482 0.0413893i
\(857\) −32.9168 −1.12442 −0.562208 0.826996i \(-0.690048\pi\)
−0.562208 + 0.826996i \(0.690048\pi\)
\(858\) 0 0
\(859\) −28.4747 −0.971543 −0.485772 0.874086i \(-0.661461\pi\)
−0.485772 + 0.874086i \(0.661461\pi\)
\(860\) −0.0603091 0.185612i −0.00205652 0.00632933i
\(861\) 23.8921 + 17.3586i 0.814241 + 0.591581i
\(862\) −33.8246 + 24.5750i −1.15207 + 0.837029i
\(863\) 9.04709 27.8441i 0.307966 0.947823i −0.670587 0.741831i \(-0.733958\pi\)
0.978554 0.205992i \(-0.0660422\pi\)
\(864\) −12.0454 + 37.0720i −0.409793 + 1.26121i
\(865\) 0.192474 0.139841i 0.00654432 0.00475473i
\(866\) −61.0141 44.3293i −2.07334 1.50637i
\(867\) −12.2111 37.5818i −0.414709 1.27634i
\(868\) 7.77363 0.263854
\(869\) 0 0
\(870\) 0.951826 0.0322699
\(871\) −4.24275 13.0579i −0.143760 0.442449i
\(872\) −0.374149 0.271835i −0.0126703 0.00920551i
\(873\) −13.0914 + 9.51146i −0.443077 + 0.321914i
\(874\) 6.79317 20.9072i 0.229782 0.707198i
\(875\) 0.0831947 0.256047i 0.00281250 0.00865597i
\(876\) 45.7446 33.2354i 1.54557 1.12292i
\(877\) 18.2858 + 13.2854i 0.617468 + 0.448617i 0.852036 0.523483i \(-0.175368\pi\)
−0.234568 + 0.972100i \(0.575368\pi\)
\(878\) −23.1610 71.2823i −0.781647 2.40566i
\(879\) 15.3738 0.518544
\(880\) 0 0
\(881\) −35.1102 −1.18289 −0.591447 0.806344i \(-0.701443\pi\)
−0.591447 + 0.806344i \(0.701443\pi\)
\(882\) 2.92151 + 8.99149i 0.0983724 + 0.302759i
\(883\) −12.2996 8.93621i −0.413916 0.300727i 0.361269 0.932461i \(-0.382343\pi\)
−0.775185 + 0.631734i \(0.782343\pi\)
\(884\) 12.8497 9.33582i 0.432181 0.313998i
\(885\) −0.225576 + 0.694251i −0.00758264 + 0.0233370i
\(886\) −0.630372 + 1.94009i −0.0211778 + 0.0651785i
\(887\) 31.1728 22.6483i 1.04668 0.760457i 0.0751006 0.997176i \(-0.476072\pi\)
0.971578 + 0.236719i \(0.0760722\pi\)
\(888\) 0.143818 + 0.104490i 0.00482621 + 0.00350645i
\(889\) −1.55475 4.78503i −0.0521447 0.160485i
\(890\) −0.0650753 −0.00218133
\(891\) 0 0
\(892\) −12.6632 −0.423995
\(893\) −3.80376 11.7068i −0.127288 0.391752i
\(894\) 13.9863 + 10.1616i 0.467772 + 0.339856i
\(895\) 0.184372 0.133954i 0.00616288 0.00447760i
\(896\) 0.302558 0.931179i 0.0101078 0.0311085i
\(897\) −33.8853 + 104.288i −1.13140 + 3.48209i
\(898\) −32.3241 + 23.4849i −1.07867 + 0.783700i
\(899\) 20.7432 + 15.0708i 0.691825 + 0.502641i
\(900\) −14.2653 43.9041i −0.475510 1.46347i
\(901\) −6.64893 −0.221508
\(902\) 0 0
\(903\) 10.4202 0.346764
\(904\) −0.240220 0.739322i −0.00798961 0.0245895i
\(905\) −0.527148 0.382995i −0.0175230 0.0127312i
\(906\) −88.2255 + 64.0996i −2.93110 + 2.12957i
\(907\) −17.4352 + 53.6600i −0.578926 + 1.78175i 0.0434788 + 0.999054i \(0.486156\pi\)
−0.622405 + 0.782696i \(0.713844\pi\)
\(908\) 8.15058 25.0849i 0.270486 0.832471i
\(909\) 15.6030 11.3362i 0.517518 0.375998i
\(910\) −0.210997 0.153298i −0.00699448 0.00508179i
\(911\) −9.45295 29.0932i −0.313190 0.963900i −0.976493 0.215549i \(-0.930846\pi\)
0.663303 0.748351i \(-0.269154\pi\)
\(912\) −15.7712 −0.522237
\(913\) 0 0
\(914\) −47.9173 −1.58496
\(915\) −0.196296 0.604136i −0.00648934 0.0199721i
\(916\) 30.4545 + 22.1265i 1.00625 + 0.731080i
\(917\) 3.04480 2.21217i 0.100548 0.0730524i
\(918\) 5.06021 15.5737i 0.167012 0.514010i
\(919\) 10.1637 31.2806i 0.335269 1.03185i −0.631320 0.775522i \(-0.717487\pi\)
0.966589 0.256330i \(-0.0825133\pi\)
\(920\) −0.0215037 + 0.0156234i −0.000708957 + 0.000515088i
\(921\) −19.4088 14.1013i −0.639542 0.464654i
\(922\) 7.10664 + 21.8720i 0.234045 + 0.720316i
\(923\) −9.98437 −0.328640
\(924\) 0 0
\(925\) −2.60481 −0.0856457
\(926\) 13.2509 + 40.7820i 0.435451 + 1.34018i
\(927\) 15.2353 + 11.0691i 0.500394 + 0.363557i
\(928\) −41.0180 + 29.8013i −1.34648 + 0.978275i
\(929\) 6.74665 20.7641i 0.221350 0.681246i −0.777291 0.629141i \(-0.783407\pi\)
0.998642 0.0521055i \(-0.0165932\pi\)
\(930\) −0.184513 + 0.567873i −0.00605042 + 0.0186213i
\(931\) −1.11154 + 0.807582i −0.0364293 + 0.0264674i
\(932\) −6.83935 4.96908i −0.224030 0.162767i
\(933\) 16.4682 + 50.6838i 0.539144 + 1.65931i
\(934\) 31.5835 1.03344
\(935\) 0 0
\(936\) 2.84730 0.0930670
\(937\) −10.8008 33.2416i −0.352848 1.08596i −0.957247 0.289273i \(-0.906586\pi\)
0.604398 0.796682i \(-0.293414\pi\)
\(938\) −4.51604 3.28110i −0.147454 0.107132i
\(939\) 1.36777 0.993744i 0.0446355 0.0324296i
\(940\) 0.144481 0.444667i 0.00471245 0.0145034i
\(941\) −6.31028 + 19.4210i −0.205709 + 0.633108i 0.793974 + 0.607951i \(0.208008\pi\)
−0.999684 + 0.0251567i \(0.991992\pi\)
\(942\) 102.689 74.6079i 3.34579 2.43086i
\(943\) 69.1321 + 50.2274i 2.25125 + 1.63563i
\(944\) −12.3868 38.1227i −0.403156 1.24079i
\(945\) −0.132338 −0.00430494
\(946\) 0 0
\(947\) −11.3122 −0.367597 −0.183799 0.982964i \(-0.558839\pi\)
−0.183799 + 0.982964i \(0.558839\pi\)
\(948\) 9.77211 + 30.0755i 0.317383 + 0.976806i
\(949\) −41.3424 30.0370i −1.34203 0.975044i
\(950\) 11.0278 8.01213i 0.357788 0.259948i
\(951\) −4.48847 + 13.8141i −0.145549 + 0.447952i
\(952\) −0.0635213 + 0.195499i −0.00205874 + 0.00633614i
\(953\) 3.68847 2.67983i 0.119481 0.0868081i −0.526440 0.850212i \(-0.676474\pi\)
0.645921 + 0.763404i \(0.276474\pi\)
\(954\) 30.2929 + 22.0091i 0.980769 + 0.712570i
\(955\) 0.0647899 + 0.199403i 0.00209655 + 0.00645252i
\(956\) 20.5268 0.663885
\(957\) 0 0
\(958\) 10.4856 0.338775
\(959\) 5.91393 + 18.2012i 0.190971 + 0.587747i
\(960\) −0.455145 0.330682i −0.0146897 0.0106727i
\(961\) 12.0669 8.76714i 0.389256 0.282811i
\(962\) −1.55964 + 4.80009i −0.0502849 + 0.154761i
\(963\) 15.3083 47.1142i 0.493304 1.51823i
\(964\) −29.3060 + 21.2921i −0.943883 + 0.685771i
\(965\) 0.371685 + 0.270045i 0.0119650 + 0.00869305i
\(966\) 13.7768 + 42.4005i 0.443260 + 1.36421i
\(967\) −38.9153 −1.25143 −0.625715 0.780052i \(-0.715193\pi\)
−0.625715 + 0.780052i \(0.715193\pi\)
\(968\) 0 0
\(969\) 6.42694 0.206463
\(970\) −0.0560840 0.172609i −0.00180075 0.00554214i
\(971\) −34.2545 24.8874i −1.09928 0.798674i −0.118338 0.992973i \(-0.537757\pi\)
−0.980942 + 0.194300i \(0.937757\pi\)
\(972\) 25.7285 18.6928i 0.825241 0.599573i
\(973\) 1.08498 3.33924i 0.0347830 0.107051i
\(974\) −16.5979 + 51.0831i −0.531832 + 1.63681i
\(975\) −55.0081 + 39.9657i −1.76167 + 1.27993i
\(976\) 28.2198 + 20.5028i 0.903292 + 0.656280i
\(977\) 11.0188 + 33.9123i 0.352522 + 1.08495i 0.957433 + 0.288657i \(0.0932088\pi\)
−0.604911 + 0.796293i \(0.706791\pi\)
\(978\) 105.003 3.35762
\(979\) 0 0
\(980\) −0.0521874 −0.00166707
\(981\) −5.56028 17.1128i −0.177526 0.546369i
\(982\) −30.1835 21.9296i −0.963193 0.699801i
\(983\) 23.8832 17.3522i 0.761756 0.553448i −0.137692 0.990475i \(-0.543968\pi\)
0.899449 + 0.437027i \(0.143968\pi\)
\(984\) 1.11744 3.43911i 0.0356226 0.109635i
\(985\) 0.0503810 0.155057i 0.00160527 0.00494052i
\(986\) 17.2314 12.5194i 0.548760 0.398698i
\(987\) 20.1959 + 14.6732i 0.642842 + 0.467052i
\(988\) −4.01690 12.3627i −0.127794 0.393311i
\(989\) 30.1511 0.958748
\(990\) 0 0
\(991\) −30.7292 −0.976145 −0.488072 0.872803i \(-0.662300\pi\)
−0.488072 + 0.872803i \(0.662300\pi\)
\(992\) −9.82848 30.2489i −0.312054 0.960405i
\(993\) −1.50811 1.09571i −0.0478586 0.0347713i
\(994\) −3.28408 + 2.38602i −0.104165 + 0.0756800i
\(995\) 0.114136 0.351274i 0.00361835 0.0111361i
\(996\) 4.34843 13.3831i 0.137785 0.424060i
\(997\) −40.4474 + 29.3868i −1.28098 + 0.930688i −0.999582 0.0289020i \(-0.990799\pi\)
−0.281400 + 0.959590i \(0.590799\pi\)
\(998\) 63.8456 + 46.3866i 2.02100 + 1.46834i
\(999\) 0.791389 + 2.43564i 0.0250384 + 0.0770604i
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 847.2.f.w.148.4 16
11.2 odd 10 847.2.f.v.372.1 16
11.3 even 5 847.2.a.p.1.7 8
11.4 even 5 77.2.f.b.36.1 yes 16
11.5 even 5 77.2.f.b.15.1 16
11.6 odd 10 847.2.f.x.323.4 16
11.7 odd 10 847.2.f.x.729.4 16
11.8 odd 10 847.2.a.o.1.2 8
11.9 even 5 inner 847.2.f.w.372.4 16
11.10 odd 2 847.2.f.v.148.1 16
33.5 odd 10 693.2.m.i.631.4 16
33.8 even 10 7623.2.a.cw.1.7 8
33.14 odd 10 7623.2.a.ct.1.2 8
33.26 odd 10 693.2.m.i.190.4 16
77.4 even 15 539.2.q.g.520.1 32
77.5 odd 30 539.2.q.f.312.1 32
77.16 even 15 539.2.q.g.312.1 32
77.26 odd 30 539.2.q.f.410.4 32
77.27 odd 10 539.2.f.e.246.1 16
77.37 even 15 539.2.q.g.410.4 32
77.38 odd 30 539.2.q.f.422.4 32
77.41 even 10 5929.2.a.bs.1.2 8
77.48 odd 10 539.2.f.e.344.1 16
77.59 odd 30 539.2.q.f.520.1 32
77.60 even 15 539.2.q.g.422.4 32
77.69 odd 10 5929.2.a.bt.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.15.1 16 11.5 even 5
77.2.f.b.36.1 yes 16 11.4 even 5
539.2.f.e.246.1 16 77.27 odd 10
539.2.f.e.344.1 16 77.48 odd 10
539.2.q.f.312.1 32 77.5 odd 30
539.2.q.f.410.4 32 77.26 odd 30
539.2.q.f.422.4 32 77.38 odd 30
539.2.q.f.520.1 32 77.59 odd 30
539.2.q.g.312.1 32 77.16 even 15
539.2.q.g.410.4 32 77.37 even 15
539.2.q.g.422.4 32 77.60 even 15
539.2.q.g.520.1 32 77.4 even 15
693.2.m.i.190.4 16 33.26 odd 10
693.2.m.i.631.4 16 33.5 odd 10
847.2.a.o.1.2 8 11.8 odd 10
847.2.a.p.1.7 8 11.3 even 5
847.2.f.v.148.1 16 11.10 odd 2
847.2.f.v.372.1 16 11.2 odd 10
847.2.f.w.148.4 16 1.1 even 1 trivial
847.2.f.w.372.4 16 11.9 even 5 inner
847.2.f.x.323.4 16 11.6 odd 10
847.2.f.x.729.4 16 11.7 odd 10
5929.2.a.bs.1.2 8 77.41 even 10
5929.2.a.bt.1.7 8 77.69 odd 10
7623.2.a.ct.1.2 8 33.14 odd 10
7623.2.a.cw.1.7 8 33.8 even 10