Properties

Label 784.2.x.l.557.3
Level $784$
Weight $2$
Character 784.557
Analytic conductor $6.260$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), 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: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 557.3
Character \(\chi\) \(=\) 784.557
Dual form 784.2.x.l.373.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.966164 + 1.03273i) q^{2} +(-3.02670 + 0.811002i) q^{3} +(-0.133053 - 1.99557i) q^{4} +(0.537019 + 0.143894i) q^{5} +(2.08675 - 3.90932i) q^{6} +(2.18943 + 1.79064i) q^{8} +(5.90511 - 3.40932i) q^{9} +O(q^{10})\) \(q+(-0.966164 + 1.03273i) q^{2} +(-3.02670 + 0.811002i) q^{3} +(-0.133053 - 1.99557i) q^{4} +(0.537019 + 0.143894i) q^{5} +(2.08675 - 3.90932i) q^{6} +(2.18943 + 1.79064i) q^{8} +(5.90511 - 3.40932i) q^{9} +(-0.667452 + 0.415570i) q^{10} +(0.814781 + 3.04081i) q^{11} +(2.02112 + 5.93208i) q^{12} +(-3.16316 - 3.16316i) q^{13} -1.74209 q^{15} +(-3.96459 + 0.531034i) q^{16} +(-0.490475 + 0.849528i) q^{17} +(-2.18441 + 9.39233i) q^{18} +(-1.92687 + 7.19116i) q^{19} +(0.215698 - 1.09080i) q^{20} +(-3.92754 - 2.09647i) q^{22} +(-1.09077 + 0.629754i) q^{23} +(-8.07896 - 3.64410i) q^{24} +(-4.06244 - 2.34545i) q^{25} +(6.32282 - 0.210551i) q^{26} +(-8.46094 + 8.46094i) q^{27} +(3.17349 + 3.17349i) q^{29} +(1.68315 - 1.79911i) q^{30} +(2.21570 - 3.83770i) q^{31} +(3.28204 - 4.60741i) q^{32} +(-4.93220 - 8.54282i) q^{33} +(-0.403452 - 1.32731i) q^{34} +(-7.58922 - 11.3304i) q^{36} +(-0.881285 - 0.236140i) q^{37} +(-5.56484 - 8.93777i) q^{38} +(12.1393 + 7.00862i) q^{39} +(0.918105 + 1.27665i) q^{40} +1.21375i q^{41} +(0.966515 - 0.966515i) q^{43} +(5.95973 - 2.03054i) q^{44} +(3.66174 - 0.981160i) q^{45} +(0.403495 - 1.73491i) q^{46} +(-4.98574 - 8.63555i) q^{47} +(11.5690 - 4.82257i) q^{48} +(6.34720 - 1.92931i) q^{50} +(0.795553 - 2.96904i) q^{51} +(-5.89144 + 6.73318i) q^{52} +(-2.95681 - 11.0350i) q^{53} +(-0.563190 - 16.9125i) q^{54} +1.75021i q^{55} -23.3282i q^{57} +(-6.34346 + 0.211239i) q^{58} +(0.663915 + 2.47776i) q^{59} +(0.231791 + 3.47647i) q^{60} +(-0.947210 + 3.53504i) q^{61} +(1.82257 + 5.99606i) q^{62} +(1.58722 + 7.84097i) q^{64} +(-1.24352 - 2.15384i) q^{65} +(13.5877 + 3.16015i) q^{66} +(2.17555 - 0.582936i) q^{67} +(1.76055 + 0.865745i) q^{68} +(2.79069 - 2.79069i) q^{69} +0.934634i q^{71} +(19.0337 + 3.10946i) q^{72} +(-0.615321 - 0.355256i) q^{73} +(1.09533 - 0.681978i) q^{74} +(14.1980 + 3.80433i) q^{75} +(14.6068 + 2.88839i) q^{76} +(-18.9665 + 5.76510i) q^{78} +(-5.93220 - 10.2749i) q^{79} +(-2.20548 - 0.285305i) q^{80} +(8.51894 - 14.7552i) q^{81} +(-1.25347 - 1.17268i) q^{82} +(-6.77482 - 6.77482i) q^{83} +(-0.385637 + 0.385637i) q^{85} +(0.0643346 + 1.93196i) q^{86} +(-12.1789 - 7.03150i) q^{87} +(-3.66108 + 8.11661i) q^{88} +(8.84053 - 5.10408i) q^{89} +(-2.52457 + 4.72954i) q^{90} +(1.40185 + 2.09291i) q^{92} +(-3.59387 + 13.4125i) q^{93} +(13.7352 + 3.19445i) q^{94} +(-2.06953 + 3.58453i) q^{95} +(-6.19712 + 16.6070i) q^{96} -3.03684 q^{97} +(15.1784 + 15.1784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.966164 + 1.03273i −0.683181 + 0.730249i
\(3\) −3.02670 + 0.811002i −1.74747 + 0.468232i −0.984082 0.177713i \(-0.943130\pi\)
−0.763384 + 0.645945i \(0.776463\pi\)
\(4\) −0.133053 1.99557i −0.0665266 0.997785i
\(5\) 0.537019 + 0.143894i 0.240162 + 0.0643513i 0.376892 0.926257i \(-0.376993\pi\)
−0.136730 + 0.990608i \(0.543659\pi\)
\(6\) 2.08675 3.90932i 0.851910 1.59597i
\(7\) 0 0
\(8\) 2.18943 + 1.79064i 0.774081 + 0.633087i
\(9\) 5.90511 3.40932i 1.96837 1.13644i
\(10\) −0.667452 + 0.415570i −0.211067 + 0.131415i
\(11\) 0.814781 + 3.04081i 0.245666 + 0.916837i 0.973048 + 0.230604i \(0.0740703\pi\)
−0.727382 + 0.686233i \(0.759263\pi\)
\(12\) 2.02112 + 5.93208i 0.583448 + 1.71244i
\(13\) −3.16316 3.16316i −0.877304 0.877304i 0.115951 0.993255i \(-0.463008\pi\)
−0.993255 + 0.115951i \(0.963008\pi\)
\(14\) 0 0
\(15\) −1.74209 −0.449807
\(16\) −3.96459 + 0.531034i −0.991148 + 0.132758i
\(17\) −0.490475 + 0.849528i −0.118958 + 0.206041i −0.919355 0.393429i \(-0.871289\pi\)
0.800397 + 0.599470i \(0.204622\pi\)
\(18\) −2.18441 + 9.39233i −0.514871 + 2.21379i
\(19\) −1.92687 + 7.19116i −0.442053 + 1.64977i 0.281548 + 0.959547i \(0.409152\pi\)
−0.723601 + 0.690218i \(0.757515\pi\)
\(20\) 0.215698 1.09080i 0.0482315 0.243911i
\(21\) 0 0
\(22\) −3.92754 2.09647i −0.837354 0.446969i
\(23\) −1.09077 + 0.629754i −0.227441 + 0.131313i −0.609391 0.792870i \(-0.708586\pi\)
0.381950 + 0.924183i \(0.375253\pi\)
\(24\) −8.07896 3.64410i −1.64911 0.743848i
\(25\) −4.06244 2.34545i −0.812489 0.469090i
\(26\) 6.32282 0.210551i 1.24001 0.0412925i
\(27\) −8.46094 + 8.46094i −1.62831 + 1.62831i
\(28\) 0 0
\(29\) 3.17349 + 3.17349i 0.589302 + 0.589302i 0.937443 0.348140i \(-0.113187\pi\)
−0.348140 + 0.937443i \(0.613187\pi\)
\(30\) 1.68315 1.79911i 0.307300 0.328471i
\(31\) 2.21570 3.83770i 0.397951 0.689272i −0.595522 0.803339i \(-0.703055\pi\)
0.993473 + 0.114068i \(0.0363880\pi\)
\(32\) 3.28204 4.60741i 0.580187 0.814483i
\(33\) −4.93220 8.54282i −0.858585 1.48711i
\(34\) −0.403452 1.32731i −0.0691914 0.227632i
\(35\) 0 0
\(36\) −7.58922 11.3304i −1.26487 1.88841i
\(37\) −0.881285 0.236140i −0.144882 0.0388211i 0.185649 0.982616i \(-0.440561\pi\)
−0.330531 + 0.943795i \(0.607228\pi\)
\(38\) −5.56484 8.93777i −0.902737 1.44990i
\(39\) 12.1393 + 7.00862i 1.94384 + 1.12228i
\(40\) 0.918105 + 1.27665i 0.145165 + 0.201857i
\(41\) 1.21375i 0.189556i 0.995498 + 0.0947779i \(0.0302141\pi\)
−0.995498 + 0.0947779i \(0.969786\pi\)
\(42\) 0 0
\(43\) 0.966515 0.966515i 0.147392 0.147392i −0.629560 0.776952i \(-0.716765\pi\)
0.776952 + 0.629560i \(0.216765\pi\)
\(44\) 5.95973 2.03054i 0.898463 0.306116i
\(45\) 3.66174 0.981160i 0.545860 0.146263i
\(46\) 0.403495 1.73491i 0.0594921 0.255799i
\(47\) −4.98574 8.63555i −0.727244 1.25962i −0.958043 0.286623i \(-0.907467\pi\)
0.230799 0.973001i \(-0.425866\pi\)
\(48\) 11.5690 4.82257i 1.66984 0.696078i
\(49\) 0 0
\(50\) 6.34720 1.92931i 0.897630 0.272845i
\(51\) 0.795553 2.96904i 0.111400 0.415749i
\(52\) −5.89144 + 6.73318i −0.816996 + 0.933724i
\(53\) −2.95681 11.0350i −0.406149 1.51577i −0.801928 0.597421i \(-0.796192\pi\)
0.395779 0.918346i \(-0.370475\pi\)
\(54\) −0.563190 16.9125i −0.0766404 2.30150i
\(55\) 1.75021i 0.235999i
\(56\) 0 0
\(57\) 23.3282i 3.08989i
\(58\) −6.34346 + 0.211239i −0.832938 + 0.0277370i
\(59\) 0.663915 + 2.47776i 0.0864344 + 0.322577i 0.995582 0.0938966i \(-0.0299323\pi\)
−0.909148 + 0.416474i \(0.863266\pi\)
\(60\) 0.231791 + 3.47647i 0.0299241 + 0.448810i
\(61\) −0.947210 + 3.53504i −0.121278 + 0.452615i −0.999680 0.0253078i \(-0.991943\pi\)
0.878402 + 0.477923i \(0.158610\pi\)
\(62\) 1.82257 + 5.99606i 0.231467 + 0.761501i
\(63\) 0 0
\(64\) 1.58722 + 7.84097i 0.198402 + 0.980121i
\(65\) −1.24352 2.15384i −0.154240 0.267151i
\(66\) 13.5877 + 3.16015i 1.67253 + 0.388987i
\(67\) 2.17555 0.582936i 0.265785 0.0712170i −0.123465 0.992349i \(-0.539401\pi\)
0.389251 + 0.921132i \(0.372734\pi\)
\(68\) 1.76055 + 0.865745i 0.213498 + 0.104987i
\(69\) 2.79069 2.79069i 0.335960 0.335960i
\(70\) 0 0
\(71\) 0.934634i 0.110921i 0.998461 + 0.0554603i \(0.0176626\pi\)
−0.998461 + 0.0554603i \(0.982337\pi\)
\(72\) 19.0337 + 3.10946i 2.24314 + 0.366454i
\(73\) −0.615321 0.355256i −0.0720179 0.0415795i 0.463559 0.886066i \(-0.346572\pi\)
−0.535577 + 0.844487i \(0.679906\pi\)
\(74\) 1.09533 0.681978i 0.127330 0.0792783i
\(75\) 14.1980 + 3.80433i 1.63944 + 0.439286i
\(76\) 14.6068 + 2.88839i 1.67552 + 0.331321i
\(77\) 0 0
\(78\) −18.9665 + 5.76510i −2.14754 + 0.652769i
\(79\) −5.93220 10.2749i −0.667424 1.15601i −0.978622 0.205668i \(-0.934063\pi\)
0.311198 0.950345i \(-0.399270\pi\)
\(80\) −2.20548 0.285305i −0.246580 0.0318981i
\(81\) 8.51894 14.7552i 0.946549 1.63947i
\(82\) −1.25347 1.17268i −0.138423 0.129501i
\(83\) −6.77482 6.77482i −0.743634 0.743634i 0.229642 0.973275i \(-0.426245\pi\)
−0.973275 + 0.229642i \(0.926245\pi\)
\(84\) 0 0
\(85\) −0.385637 + 0.385637i −0.0418282 + 0.0418282i
\(86\) 0.0643346 + 1.93196i 0.00693738 + 0.208329i
\(87\) −12.1789 7.03150i −1.30572 0.753856i
\(88\) −3.66108 + 8.11661i −0.390272 + 0.865234i
\(89\) 8.84053 5.10408i 0.937095 0.541032i 0.0480464 0.998845i \(-0.484700\pi\)
0.889048 + 0.457813i \(0.151367\pi\)
\(90\) −2.52457 + 4.72954i −0.266113 + 0.498537i
\(91\) 0 0
\(92\) 1.40185 + 2.09291i 0.146153 + 0.218201i
\(93\) −3.59387 + 13.4125i −0.372667 + 1.39081i
\(94\) 13.7352 + 3.19445i 1.41668 + 0.329482i
\(95\) −2.06953 + 3.58453i −0.212329 + 0.367765i
\(96\) −6.19712 + 16.6070i −0.632491 + 1.69494i
\(97\) −3.03684 −0.308344 −0.154172 0.988044i \(-0.549271\pi\)
−0.154172 + 0.988044i \(0.549271\pi\)
\(98\) 0 0
\(99\) 15.1784 + 15.1784i 1.52549 + 1.52549i
\(100\) −4.13999 + 8.41896i −0.413999 + 0.841896i
\(101\) −3.72056 13.8853i −0.370210 1.38164i −0.860219 0.509925i \(-0.829673\pi\)
0.490009 0.871717i \(-0.336993\pi\)
\(102\) 2.29758 + 3.69017i 0.227494 + 0.365382i
\(103\) 5.24395 3.02760i 0.516702 0.298318i −0.218882 0.975751i \(-0.570241\pi\)
0.735584 + 0.677433i \(0.236908\pi\)
\(104\) −1.26144 12.5896i −0.123695 1.23451i
\(105\) 0 0
\(106\) 14.2529 + 7.60800i 1.38436 + 0.738954i
\(107\) −17.0716 4.57432i −1.65037 0.442216i −0.690655 0.723184i \(-0.742678\pi\)
−0.959717 + 0.280968i \(0.909344\pi\)
\(108\) 18.0102 + 15.7586i 1.73303 + 1.51638i
\(109\) −13.7388 + 3.68130i −1.31594 + 0.352604i −0.847454 0.530868i \(-0.821866\pi\)
−0.468483 + 0.883473i \(0.655199\pi\)
\(110\) −1.80749 1.69099i −0.172338 0.161230i
\(111\) 2.85889 0.271354
\(112\) 0 0
\(113\) 5.01929 0.472175 0.236088 0.971732i \(-0.424135\pi\)
0.236088 + 0.971732i \(0.424135\pi\)
\(114\) 24.0917 + 22.5389i 2.25639 + 2.11096i
\(115\) −0.676380 + 0.181236i −0.0630728 + 0.0169003i
\(116\) 5.91068 6.75516i 0.548793 0.627201i
\(117\) −29.4631 7.89461i −2.72386 0.729857i
\(118\) −3.20031 1.70828i −0.294612 0.157260i
\(119\) 0 0
\(120\) −3.81420 3.11946i −0.348187 0.284767i
\(121\) 0.943649 0.544816i 0.0857863 0.0495287i
\(122\) −2.73557 4.39363i −0.247667 0.397781i
\(123\) −0.984353 3.67365i −0.0887561 0.331242i
\(124\) −7.95321 3.91096i −0.714219 0.351215i
\(125\) −3.80974 3.80974i −0.340754 0.340754i
\(126\) 0 0
\(127\) −19.3869 −1.72031 −0.860156 0.510031i \(-0.829634\pi\)
−0.860156 + 0.510031i \(0.829634\pi\)
\(128\) −9.63110 5.93650i −0.851277 0.524717i
\(129\) −2.14151 + 3.70920i −0.188549 + 0.326577i
\(130\) 3.42577 + 0.796745i 0.300460 + 0.0698792i
\(131\) 3.03517 11.3274i 0.265184 0.989680i −0.696954 0.717116i \(-0.745462\pi\)
0.962138 0.272564i \(-0.0878717\pi\)
\(132\) −16.3915 + 10.9792i −1.42670 + 0.955616i
\(133\) 0 0
\(134\) −1.49992 + 2.80996i −0.129574 + 0.242744i
\(135\) −5.76117 + 3.32621i −0.495842 + 0.286275i
\(136\) −2.59506 + 0.981719i −0.222525 + 0.0841817i
\(137\) 8.98270 + 5.18617i 0.767444 + 0.443084i 0.831962 0.554832i \(-0.187218\pi\)
−0.0645179 + 0.997917i \(0.520551\pi\)
\(138\) 0.185758 + 5.57829i 0.0158128 + 0.474856i
\(139\) −4.83290 + 4.83290i −0.409921 + 0.409921i −0.881711 0.471790i \(-0.843608\pi\)
0.471790 + 0.881711i \(0.343608\pi\)
\(140\) 0 0
\(141\) 22.0938 + 22.0938i 1.86063 + 1.86063i
\(142\) −0.965222 0.903010i −0.0809997 0.0757789i
\(143\) 7.04128 12.1959i 0.588821 1.01987i
\(144\) −21.6009 + 16.6524i −1.80008 + 1.38770i
\(145\) 1.24758 + 2.16087i 0.103606 + 0.179451i
\(146\) 0.961384 0.292224i 0.0795647 0.0241846i
\(147\) 0 0
\(148\) −0.353975 + 1.79008i −0.0290966 + 0.147144i
\(149\) −2.37756 0.637064i −0.194777 0.0521903i 0.160112 0.987099i \(-0.448815\pi\)
−0.354889 + 0.934909i \(0.615481\pi\)
\(150\) −17.6464 + 10.9870i −1.44082 + 0.897086i
\(151\) −18.0246 10.4065i −1.46682 0.846871i −0.467513 0.883986i \(-0.654850\pi\)
−0.999311 + 0.0371149i \(0.988183\pi\)
\(152\) −17.0955 + 12.2942i −1.38663 + 0.997194i
\(153\) 6.68874i 0.540753i
\(154\) 0 0
\(155\) 1.74209 1.74209i 0.139928 0.139928i
\(156\) 12.3710 25.1573i 0.990473 2.01420i
\(157\) 13.8571 3.71300i 1.10592 0.296330i 0.340746 0.940155i \(-0.389320\pi\)
0.765172 + 0.643825i \(0.222654\pi\)
\(158\) 16.3426 + 3.80086i 1.30015 + 0.302381i
\(159\) 17.8987 + 31.0015i 1.41946 + 2.45858i
\(160\) 2.42549 2.00200i 0.191752 0.158272i
\(161\) 0 0
\(162\) 7.00745 + 23.0537i 0.550557 + 1.81127i
\(163\) −4.35137 + 16.2395i −0.340825 + 1.27198i 0.556589 + 0.830788i \(0.312110\pi\)
−0.897414 + 0.441190i \(0.854557\pi\)
\(164\) 2.42212 0.161493i 0.189136 0.0126105i
\(165\) −1.41943 5.29737i −0.110502 0.412400i
\(166\) 13.5421 0.450956i 1.05107 0.0350010i
\(167\) 1.10868i 0.0857923i 0.999080 + 0.0428962i \(0.0136585\pi\)
−0.999080 + 0.0428962i \(0.986342\pi\)
\(168\) 0 0
\(169\) 7.01121i 0.539324i
\(170\) −0.0256693 0.770846i −0.00196875 0.0591212i
\(171\) 13.1386 + 49.0339i 1.00473 + 3.74972i
\(172\) −2.05735 1.80015i −0.156871 0.137260i
\(173\) −2.64992 + 9.88962i −0.201469 + 0.751894i 0.789027 + 0.614358i \(0.210585\pi\)
−0.990497 + 0.137536i \(0.956082\pi\)
\(174\) 19.0284 5.78392i 1.44254 0.438478i
\(175\) 0 0
\(176\) −4.84505 11.6229i −0.365209 0.876108i
\(177\) −4.01894 6.96101i −0.302082 0.523222i
\(178\) −3.27028 + 14.0612i −0.245118 + 1.05394i
\(179\) −13.5777 + 3.63814i −1.01485 + 0.271928i −0.727654 0.685945i \(-0.759389\pi\)
−0.287194 + 0.957872i \(0.592722\pi\)
\(180\) −2.44518 7.17671i −0.182253 0.534920i
\(181\) 7.35342 7.35342i 0.546576 0.546576i −0.378873 0.925449i \(-0.623688\pi\)
0.925449 + 0.378873i \(0.123688\pi\)
\(182\) 0 0
\(183\) 11.4677i 0.847715i
\(184\) −3.51582 0.574366i −0.259190 0.0423429i
\(185\) −0.439288 0.253623i −0.0322971 0.0186467i
\(186\) −10.3792 16.6702i −0.761040 1.22232i
\(187\) −2.98288 0.799260i −0.218130 0.0584477i
\(188\) −16.5695 + 11.0984i −1.20845 + 0.809432i
\(189\) 0 0
\(190\) −1.70234 5.60050i −0.123501 0.406303i
\(191\) −1.77342 3.07165i −0.128320 0.222257i 0.794706 0.606995i \(-0.207625\pi\)
−0.923026 + 0.384738i \(0.874292\pi\)
\(192\) −11.1631 22.4450i −0.805625 1.61983i
\(193\) −1.49697 + 2.59283i −0.107754 + 0.186636i −0.914860 0.403771i \(-0.867699\pi\)
0.807106 + 0.590407i \(0.201033\pi\)
\(194\) 2.93409 3.13623i 0.210655 0.225168i
\(195\) 5.51053 + 5.51053i 0.394617 + 0.394617i
\(196\) 0 0
\(197\) 3.55345 3.55345i 0.253173 0.253173i −0.569097 0.822270i \(-0.692707\pi\)
0.822270 + 0.569097i \(0.192707\pi\)
\(198\) −30.3401 + 1.01033i −2.15618 + 0.0718011i
\(199\) 1.55979 + 0.900545i 0.110571 + 0.0638380i 0.554265 0.832340i \(-0.312999\pi\)
−0.443695 + 0.896178i \(0.646333\pi\)
\(200\) −4.69458 12.4096i −0.331957 0.877490i
\(201\) −6.11197 + 3.52875i −0.431105 + 0.248899i
\(202\) 17.9344 + 9.57318i 1.26186 + 0.673567i
\(203\) 0 0
\(204\) −6.03078 1.19254i −0.422239 0.0834945i
\(205\) −0.174651 + 0.651807i −0.0121982 + 0.0455242i
\(206\) −1.93984 + 8.34074i −0.135155 + 0.581127i
\(207\) −4.29407 + 7.43754i −0.298458 + 0.516945i
\(208\) 14.2204 + 10.8609i 0.986008 + 0.753069i
\(209\) −23.4369 −1.62116
\(210\) 0 0
\(211\) −15.1022 15.1022i −1.03968 1.03968i −0.999180 0.0404953i \(-0.987106\pi\)
−0.0404953 0.999180i \(-0.512894\pi\)
\(212\) −21.6276 + 7.36875i −1.48539 + 0.506088i
\(213\) −0.757990 2.82886i −0.0519366 0.193830i
\(214\) 21.2180 13.2108i 1.45043 0.903069i
\(215\) 0.658113 0.379962i 0.0448829 0.0259132i
\(216\) −33.6752 + 3.37415i −2.29130 + 0.229582i
\(217\) 0 0
\(218\) 9.47215 17.7452i 0.641535 1.20185i
\(219\) 2.15050 + 0.576226i 0.145318 + 0.0389377i
\(220\) 3.49267 0.232872i 0.235476 0.0157002i
\(221\) 4.23865 1.13574i 0.285123 0.0763983i
\(222\) −2.76216 + 2.95246i −0.185384 + 0.198156i
\(223\) 7.11258 0.476294 0.238147 0.971229i \(-0.423460\pi\)
0.238147 + 0.971229i \(0.423460\pi\)
\(224\) 0 0
\(225\) −31.9856 −2.13237
\(226\) −4.84946 + 5.18356i −0.322581 + 0.344806i
\(227\) 16.6228 4.45405i 1.10329 0.295626i 0.339187 0.940719i \(-0.389848\pi\)
0.764104 + 0.645093i \(0.223181\pi\)
\(228\) −46.5530 + 3.10389i −3.08305 + 0.205560i
\(229\) 0.848962 + 0.227479i 0.0561010 + 0.0150322i 0.286760 0.958002i \(-0.407422\pi\)
−0.230659 + 0.973035i \(0.574088\pi\)
\(230\) 0.466328 0.873620i 0.0307487 0.0576048i
\(231\) 0 0
\(232\) 1.26556 + 12.6307i 0.0830881 + 0.829247i
\(233\) 4.20619 2.42844i 0.275556 0.159093i −0.355854 0.934542i \(-0.615810\pi\)
0.631410 + 0.775449i \(0.282477\pi\)
\(234\) 36.6191 22.7998i 2.39387 1.49047i
\(235\) −1.43483 5.35487i −0.0935982 0.349313i
\(236\) 4.85621 1.65456i 0.316113 0.107703i
\(237\) 26.2879 + 26.2879i 1.70758 + 1.70758i
\(238\) 0 0
\(239\) 4.91033 0.317623 0.158811 0.987309i \(-0.449234\pi\)
0.158811 + 0.987309i \(0.449234\pi\)
\(240\) 6.90670 0.925111i 0.445825 0.0597157i
\(241\) −5.42956 + 9.40428i −0.349749 + 0.605783i −0.986205 0.165530i \(-0.947066\pi\)
0.636456 + 0.771313i \(0.280400\pi\)
\(242\) −0.349073 + 1.50091i −0.0224393 + 0.0964824i
\(243\) −4.52699 + 16.8950i −0.290407 + 1.08381i
\(244\) 7.18044 + 1.41987i 0.459680 + 0.0908982i
\(245\) 0 0
\(246\) 4.74493 + 2.53279i 0.302526 + 0.161484i
\(247\) 28.8418 16.6518i 1.83516 1.05953i
\(248\) 11.7231 4.43487i 0.744415 0.281614i
\(249\) 25.9998 + 15.0110i 1.64767 + 0.951281i
\(250\) 7.61526 0.253590i 0.481631 0.0160384i
\(251\) 8.18516 8.18516i 0.516643 0.516643i −0.399911 0.916554i \(-0.630959\pi\)
0.916554 + 0.399911i \(0.130959\pi\)
\(252\) 0 0
\(253\) −2.80370 2.80370i −0.176267 0.176267i
\(254\) 18.7310 20.0214i 1.17528 1.25626i
\(255\) 0.854454 1.47996i 0.0535080 0.0926786i
\(256\) 15.4360 4.21067i 0.964750 0.263167i
\(257\) −10.3065 17.8514i −0.642902 1.11354i −0.984782 0.173795i \(-0.944397\pi\)
0.341880 0.939744i \(-0.388936\pi\)
\(258\) −1.76154 5.79529i −0.109669 0.360799i
\(259\) 0 0
\(260\) −4.13268 + 2.76811i −0.256298 + 0.171671i
\(261\) 29.5593 + 7.92038i 1.82967 + 0.490259i
\(262\) 8.76566 + 14.0786i 0.541544 + 0.869781i
\(263\) 11.8037 + 6.81485i 0.727846 + 0.420222i 0.817634 0.575739i \(-0.195286\pi\)
−0.0897878 + 0.995961i \(0.528619\pi\)
\(264\) 4.49840 27.5357i 0.276858 1.69471i
\(265\) 6.35145i 0.390166i
\(266\) 0 0
\(267\) −22.6182 + 22.6182i −1.38421 + 1.38421i
\(268\) −1.45275 4.26389i −0.0887410 0.260459i
\(269\) −6.05148 + 1.62149i −0.368965 + 0.0988639i −0.438537 0.898713i \(-0.644503\pi\)
0.0695721 + 0.997577i \(0.477837\pi\)
\(270\) 2.13116 9.16338i 0.129698 0.557666i
\(271\) −6.34254 10.9856i −0.385282 0.667328i 0.606526 0.795063i \(-0.292562\pi\)
−0.991808 + 0.127736i \(0.959229\pi\)
\(272\) 1.49341 3.62849i 0.0905511 0.220010i
\(273\) 0 0
\(274\) −14.0347 + 4.26600i −0.847865 + 0.257718i
\(275\) 3.82206 14.2641i 0.230479 0.860159i
\(276\) −5.94033 5.19771i −0.357566 0.312865i
\(277\) 6.25325 + 23.3375i 0.375721 + 1.40221i 0.852288 + 0.523073i \(0.175215\pi\)
−0.476566 + 0.879139i \(0.658119\pi\)
\(278\) −0.321695 9.66044i −0.0192940 0.579395i
\(279\) 30.2161i 1.80899i
\(280\) 0 0
\(281\) 12.8628i 0.767330i −0.923472 0.383665i \(-0.874662\pi\)
0.923472 0.383665i \(-0.125338\pi\)
\(282\) −44.1631 + 1.47064i −2.62987 + 0.0875753i
\(283\) −0.321770 1.20086i −0.0191272 0.0713837i 0.955703 0.294334i \(-0.0950979\pi\)
−0.974830 + 0.222950i \(0.928431\pi\)
\(284\) 1.86513 0.124356i 0.110675 0.00737918i
\(285\) 3.35678 12.5277i 0.198839 0.742076i
\(286\) 5.79196 + 19.0549i 0.342486 + 1.12674i
\(287\) 0 0
\(288\) 3.67265 38.3968i 0.216413 2.26255i
\(289\) 8.01887 + 13.8891i 0.471698 + 0.817005i
\(290\) −3.43696 0.799346i −0.201825 0.0469392i
\(291\) 9.19160 2.46288i 0.538821 0.144377i
\(292\) −0.627067 + 1.27518i −0.0366963 + 0.0746245i
\(293\) −17.9935 + 17.9935i −1.05119 + 1.05119i −0.0525765 + 0.998617i \(0.516743\pi\)
−0.998617 + 0.0525765i \(0.983257\pi\)
\(294\) 0 0
\(295\) 1.42614i 0.0830331i
\(296\) −1.50667 2.09508i −0.0875735 0.121774i
\(297\) −32.6219 18.8343i −1.89291 1.09287i
\(298\) 2.95502 1.83986i 0.171180 0.106580i
\(299\) 5.44229 + 1.45826i 0.314736 + 0.0843332i
\(300\) 5.70272 28.8392i 0.329247 1.66503i
\(301\) 0 0
\(302\) 28.1619 8.56013i 1.62053 0.492580i
\(303\) 22.5221 + 39.0093i 1.29386 + 2.24103i
\(304\) 3.82049 29.5333i 0.219120 1.69385i
\(305\) −1.01734 + 1.76208i −0.0582527 + 0.100897i
\(306\) −6.90765 6.46243i −0.394884 0.369432i
\(307\) −1.74987 1.74987i −0.0998702 0.0998702i 0.655406 0.755277i \(-0.272497\pi\)
−0.755277 + 0.655406i \(0.772497\pi\)
\(308\) 0 0
\(309\) −13.4165 + 13.4165i −0.763237 + 0.763237i
\(310\) 0.115960 + 3.48226i 0.00658608 + 0.197779i
\(311\) 15.0938 + 8.71439i 0.855889 + 0.494148i 0.862634 0.505829i \(-0.168813\pi\)
−0.00674419 + 0.999977i \(0.502147\pi\)
\(312\) 14.0282 + 37.0820i 0.794191 + 2.09935i
\(313\) −24.5458 + 14.1715i −1.38741 + 0.801021i −0.993023 0.117924i \(-0.962376\pi\)
−0.394386 + 0.918945i \(0.629043\pi\)
\(314\) −9.55373 + 17.8980i −0.539148 + 1.01004i
\(315\) 0 0
\(316\) −19.7149 + 13.2052i −1.10905 + 0.742851i
\(317\) 3.01750 11.2615i 0.169480 0.632508i −0.827946 0.560807i \(-0.810491\pi\)
0.997426 0.0717003i \(-0.0228425\pi\)
\(318\) −49.3092 11.4680i −2.76512 0.643095i
\(319\) −7.06427 + 12.2357i −0.395523 + 0.685066i
\(320\) −0.275901 + 4.43914i −0.0154233 + 0.248155i
\(321\) 55.3803 3.09103
\(322\) 0 0
\(323\) −5.16401 5.16401i −0.287333 0.287333i
\(324\) −30.5786 15.0369i −1.69881 0.835384i
\(325\) 5.43112 + 20.2692i 0.301264 + 1.12433i
\(326\) −12.5669 20.1838i −0.696015 1.11788i
\(327\) 38.5977 22.2844i 2.13446 1.23233i
\(328\) −2.17339 + 2.65742i −0.120005 + 0.146731i
\(329\) 0 0
\(330\) 6.84214 + 3.65225i 0.376647 + 0.201050i
\(331\) −0.321647 0.0861852i −0.0176793 0.00473716i 0.249969 0.968254i \(-0.419580\pi\)
−0.267648 + 0.963517i \(0.586246\pi\)
\(332\) −12.6182 + 14.4210i −0.692515 + 0.791458i
\(333\) −6.00916 + 1.61015i −0.329300 + 0.0882357i
\(334\) −1.14497 1.07117i −0.0626498 0.0586117i
\(335\) 1.25219 0.0684146
\(336\) 0 0
\(337\) 9.22099 0.502299 0.251150 0.967948i \(-0.419191\pi\)
0.251150 + 0.967948i \(0.419191\pi\)
\(338\) −7.24068 6.77398i −0.393841 0.368456i
\(339\) −15.1919 + 4.07066i −0.825111 + 0.221088i
\(340\) 0.820875 + 0.718254i 0.0445182 + 0.0389528i
\(341\) 13.4750 + 3.61062i 0.729713 + 0.195526i
\(342\) −63.3327 33.8062i −3.42464 1.82803i
\(343\) 0 0
\(344\) 3.84680 0.385438i 0.207406 0.0207814i
\(345\) 1.90022 1.09709i 0.102304 0.0590654i
\(346\) −7.65303 12.2916i −0.411430 0.660803i
\(347\) −2.93816 10.9654i −0.157729 0.588652i −0.998856 0.0478151i \(-0.984774\pi\)
0.841127 0.540837i \(-0.181892\pi\)
\(348\) −12.4114 + 25.2394i −0.665321 + 1.35297i
\(349\) 11.5879 + 11.5879i 0.620287 + 0.620287i 0.945605 0.325318i \(-0.105471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(350\) 0 0
\(351\) 53.5267 2.85704
\(352\) 16.6844 + 6.22600i 0.889281 + 0.331847i
\(353\) −9.47403 + 16.4095i −0.504252 + 0.873390i 0.495736 + 0.868473i \(0.334898\pi\)
−0.999988 + 0.00491672i \(0.998435\pi\)
\(354\) 11.0718 + 2.57501i 0.588459 + 0.136860i
\(355\) −0.134488 + 0.501916i −0.00713789 + 0.0266390i
\(356\) −11.3618 16.9628i −0.602175 0.899026i
\(357\) 0 0
\(358\) 9.36111 17.5371i 0.494750 0.926867i
\(359\) 3.06722 1.77086i 0.161882 0.0934624i −0.416871 0.908966i \(-0.636873\pi\)
0.578752 + 0.815503i \(0.303540\pi\)
\(360\) 9.77403 + 4.40867i 0.515137 + 0.232357i
\(361\) −31.5455 18.2128i −1.66029 0.958569i
\(362\) 0.489470 + 14.6987i 0.0257259 + 0.772547i
\(363\) −2.41430 + 2.41430i −0.126718 + 0.126718i
\(364\) 0 0
\(365\) −0.279320 0.279320i −0.0146203 0.0146203i
\(366\) 11.8430 + 11.0797i 0.619043 + 0.579143i
\(367\) −5.59371 + 9.68859i −0.291989 + 0.505740i −0.974280 0.225341i \(-0.927651\pi\)
0.682291 + 0.731081i \(0.260984\pi\)
\(368\) 3.99003 3.07595i 0.207994 0.160345i
\(369\) 4.13806 + 7.16732i 0.215419 + 0.373116i
\(370\) 0.686348 0.208623i 0.0356815 0.0108458i
\(371\) 0 0
\(372\) 27.2438 + 5.38724i 1.41252 + 0.279315i
\(373\) −18.8609 5.05377i −0.976581 0.261674i −0.264977 0.964255i \(-0.585364\pi\)
−0.711604 + 0.702581i \(0.752031\pi\)
\(374\) 3.70737 2.30829i 0.191704 0.119359i
\(375\) 14.6206 + 8.44123i 0.755007 + 0.435903i
\(376\) 4.54723 27.8346i 0.234506 1.43546i
\(377\) 20.0765i 1.03399i
\(378\) 0 0
\(379\) −10.9875 + 10.9875i −0.564391 + 0.564391i −0.930552 0.366161i \(-0.880672\pi\)
0.366161 + 0.930552i \(0.380672\pi\)
\(380\) 7.42853 + 3.65295i 0.381076 + 0.187393i
\(381\) 58.6784 15.7228i 3.00619 0.805505i
\(382\) 4.88559 + 1.13626i 0.249969 + 0.0581362i
\(383\) 2.41973 + 4.19109i 0.123642 + 0.214155i 0.921201 0.389086i \(-0.127209\pi\)
−0.797559 + 0.603241i \(0.793876\pi\)
\(384\) 33.9649 + 10.1572i 1.73327 + 0.518330i
\(385\) 0 0
\(386\) −1.23137 4.05106i −0.0626750 0.206194i
\(387\) 2.41222 9.00254i 0.122620 0.457625i
\(388\) 0.404061 + 6.06022i 0.0205131 + 0.307661i
\(389\) 4.56824 + 17.0489i 0.231619 + 0.864414i 0.979644 + 0.200743i \(0.0643357\pi\)
−0.748025 + 0.663671i \(0.768998\pi\)
\(390\) −11.0150 + 0.366800i −0.557764 + 0.0185736i
\(391\) 1.23552i 0.0624827i
\(392\) 0 0
\(393\) 36.7462i 1.85360i
\(394\) 0.236530 + 7.10297i 0.0119162 + 0.357842i
\(395\) −1.70721 6.37141i −0.0858992 0.320580i
\(396\) 28.2701 32.3092i 1.42063 1.62360i
\(397\) −4.30237 + 16.0566i −0.215930 + 0.805860i 0.769908 + 0.638155i \(0.220302\pi\)
−0.985837 + 0.167705i \(0.946364\pi\)
\(398\) −2.43703 + 0.740764i −0.122157 + 0.0371311i
\(399\) 0 0
\(400\) 17.3514 + 7.14147i 0.867572 + 0.357074i
\(401\) 12.7912 + 22.1549i 0.638760 + 1.10636i 0.985705 + 0.168479i \(0.0538857\pi\)
−0.346945 + 0.937885i \(0.612781\pi\)
\(402\) 2.26093 9.72135i 0.112765 0.484857i
\(403\) −19.1479 + 5.13066i −0.953825 + 0.255577i
\(404\) −27.2141 + 9.27213i −1.35395 + 0.461306i
\(405\) 6.69803 6.69803i 0.332828 0.332828i
\(406\) 0 0
\(407\) 2.87222i 0.142371i
\(408\) 7.05829 5.07597i 0.349438 0.251298i
\(409\) −16.6386 9.60629i −0.822725 0.475001i 0.0286301 0.999590i \(-0.490885\pi\)
−0.851355 + 0.524589i \(0.824219\pi\)
\(410\) −0.504397 0.810119i −0.0249104 0.0400089i
\(411\) −31.3939 8.41198i −1.54855 0.414932i
\(412\) −6.73951 10.0618i −0.332032 0.495711i
\(413\) 0 0
\(414\) −3.53218 11.6205i −0.173597 0.571116i
\(415\) −2.66336 4.61307i −0.130739 0.226447i
\(416\) −24.9556 + 4.19238i −1.22355 + 0.205549i
\(417\) 10.7082 18.5472i 0.524385 0.908261i
\(418\) 22.6439 24.2039i 1.10755 1.18385i
\(419\) 11.2764 + 11.2764i 0.550888 + 0.550888i 0.926697 0.375809i \(-0.122635\pi\)
−0.375809 + 0.926697i \(0.622635\pi\)
\(420\) 0 0
\(421\) 27.1033 27.1033i 1.32094 1.32094i 0.407918 0.913019i \(-0.366255\pi\)
0.913019 0.407918i \(-0.133745\pi\)
\(422\) 30.1876 1.00525i 1.46951 0.0489349i
\(423\) −58.8827 33.9959i −2.86297 1.65294i
\(424\) 13.2859 29.4548i 0.645220 1.43045i
\(425\) 3.98506 2.30077i 0.193304 0.111604i
\(426\) 3.65378 + 1.95034i 0.177026 + 0.0944944i
\(427\) 0 0
\(428\) −6.85694 + 34.6762i −0.331443 + 1.67614i
\(429\) −11.4210 + 42.6237i −0.551410 + 2.05789i
\(430\) −0.243448 + 1.04676i −0.0117401 + 0.0504791i
\(431\) 7.38092 12.7841i 0.355526 0.615790i −0.631682 0.775228i \(-0.717635\pi\)
0.987208 + 0.159438i \(0.0509683\pi\)
\(432\) 29.0512 38.0373i 1.39772 1.83007i
\(433\) −30.0057 −1.44198 −0.720991 0.692944i \(-0.756313\pi\)
−0.720991 + 0.692944i \(0.756313\pi\)
\(434\) 0 0
\(435\) −5.52852 5.52852i −0.265072 0.265072i
\(436\) 9.17427 + 26.9269i 0.439368 + 1.28956i
\(437\) −2.42690 9.05733i −0.116095 0.433271i
\(438\) −2.67283 + 1.66416i −0.127713 + 0.0795165i
\(439\) −29.2303 + 16.8761i −1.39509 + 0.805454i −0.993873 0.110531i \(-0.964745\pi\)
−0.401214 + 0.915984i \(0.631412\pi\)
\(440\) −3.13400 + 3.83197i −0.149408 + 0.182682i
\(441\) 0 0
\(442\) −2.92232 + 5.47469i −0.139001 + 0.260404i
\(443\) −7.13093 1.91073i −0.338800 0.0907813i 0.0854075 0.996346i \(-0.472781\pi\)
−0.424208 + 0.905565i \(0.639447\pi\)
\(444\) −0.380385 5.70512i −0.0180523 0.270753i
\(445\) 5.48198 1.46889i 0.259871 0.0696322i
\(446\) −6.87192 + 7.34536i −0.325395 + 0.347813i
\(447\) 7.71281 0.364803
\(448\) 0 0
\(449\) −1.59006 −0.0750395 −0.0375197 0.999296i \(-0.511946\pi\)
−0.0375197 + 0.999296i \(0.511946\pi\)
\(450\) 30.9033 33.0324i 1.45680 1.55716i
\(451\) −3.69078 + 0.988940i −0.173792 + 0.0465674i
\(452\) −0.667833 10.0163i −0.0314122 0.471129i
\(453\) 62.9949 + 16.8794i 2.95976 + 0.793065i
\(454\) −11.4605 + 21.4701i −0.537867 + 1.00764i
\(455\) 0 0
\(456\) 41.7724 51.0754i 1.95617 2.39183i
\(457\) 1.86124 1.07459i 0.0870651 0.0502671i −0.455835 0.890064i \(-0.650659\pi\)
0.542900 + 0.839797i \(0.317326\pi\)
\(458\) −1.05516 + 0.656965i −0.0493044 + 0.0306980i
\(459\) −3.03793 11.3377i −0.141798 0.529198i
\(460\) 0.451663 + 1.32565i 0.0210589 + 0.0618088i
\(461\) −26.7406 26.7406i −1.24543 1.24543i −0.957715 0.287719i \(-0.907103\pi\)
−0.287719 0.957715i \(-0.592897\pi\)
\(462\) 0 0
\(463\) 16.2686 0.756065 0.378033 0.925792i \(-0.376601\pi\)
0.378033 + 0.925792i \(0.376601\pi\)
\(464\) −14.2668 10.8964i −0.662321 0.505851i
\(465\) −3.85995 + 6.68564i −0.179001 + 0.310039i
\(466\) −1.55595 + 6.69012i −0.0720778 + 0.309914i
\(467\) 6.56228 24.4908i 0.303666 1.13330i −0.630421 0.776253i \(-0.717118\pi\)
0.934087 0.357044i \(-0.116216\pi\)
\(468\) −11.8341 + 59.8460i −0.547030 + 2.76638i
\(469\) 0 0
\(470\) 6.91641 + 3.69189i 0.319030 + 0.170294i
\(471\) −38.9301 + 22.4763i −1.79380 + 1.03565i
\(472\) −2.98319 + 6.61373i −0.137312 + 0.304421i
\(473\) 3.72648 + 2.15149i 0.171344 + 0.0989255i
\(474\) −52.5467 + 1.74982i −2.41355 + 0.0803717i
\(475\) 24.6943 24.6943i 1.13305 1.13305i
\(476\) 0 0
\(477\) −55.0819 55.0819i −2.52203 2.52203i
\(478\) −4.74418 + 5.07103i −0.216994 + 0.231944i
\(479\) 8.49302 14.7103i 0.388056 0.672133i −0.604132 0.796884i \(-0.706480\pi\)
0.992188 + 0.124751i \(0.0398134\pi\)
\(480\) −5.71761 + 8.02655i −0.260972 + 0.366360i
\(481\) 2.04070 + 3.53460i 0.0930479 + 0.161164i
\(482\) −4.46621 14.6933i −0.203430 0.669263i
\(483\) 0 0
\(484\) −1.21277 1.81063i −0.0551261 0.0823012i
\(485\) −1.63084 0.436983i −0.0740527 0.0198424i
\(486\) −13.0741 20.9985i −0.593053 0.952510i
\(487\) 33.8046 + 19.5171i 1.53183 + 0.884404i 0.999277 + 0.0380089i \(0.0121015\pi\)
0.532555 + 0.846395i \(0.321232\pi\)
\(488\) −8.40383 + 6.04360i −0.380423 + 0.273581i
\(489\) 52.6811i 2.38232i
\(490\) 0 0
\(491\) −26.8828 + 26.8828i −1.21320 + 1.21320i −0.243238 + 0.969967i \(0.578210\pi\)
−0.969967 + 0.243238i \(0.921790\pi\)
\(492\) −7.20006 + 2.45314i −0.324604 + 0.110596i
\(493\) −4.25249 + 1.13945i −0.191522 + 0.0513183i
\(494\) −10.6691 + 45.8741i −0.480027 + 2.06398i
\(495\) 5.96703 + 10.3352i 0.268198 + 0.464533i
\(496\) −6.74639 + 16.3915i −0.302922 + 0.736002i
\(497\) 0 0
\(498\) −40.6223 + 12.3476i −1.82033 + 0.553310i
\(499\) 1.65798 6.18767i 0.0742214 0.276998i −0.918834 0.394644i \(-0.870868\pi\)
0.993056 + 0.117646i \(0.0375347\pi\)
\(500\) −7.09570 + 8.10950i −0.317329 + 0.362668i
\(501\) −0.899143 3.35565i −0.0401707 0.149919i
\(502\) 0.544833 + 16.3613i 0.0243171 + 0.730238i
\(503\) 35.6215i 1.58829i 0.607731 + 0.794143i \(0.292080\pi\)
−0.607731 + 0.794143i \(0.707920\pi\)
\(504\) 0 0
\(505\) 7.99206i 0.355642i
\(506\) 5.60429 0.186624i 0.249141 0.00829644i
\(507\) −5.68611 21.2208i −0.252529 0.942451i
\(508\) 2.57949 + 38.6880i 0.114447 + 1.71650i
\(509\) 6.59958 24.6300i 0.292521 1.09170i −0.650645 0.759382i \(-0.725501\pi\)
0.943166 0.332322i \(-0.107832\pi\)
\(510\) 0.702851 + 2.31230i 0.0311228 + 0.102390i
\(511\) 0 0
\(512\) −10.5652 + 20.0094i −0.466922 + 0.884298i
\(513\) −44.5409 77.1471i −1.96653 3.40613i
\(514\) 28.3934 + 6.60356i 1.25238 + 0.291271i
\(515\) 3.25176 0.871306i 0.143290 0.0383943i
\(516\) 7.68690 + 3.78000i 0.338397 + 0.166405i
\(517\) 22.1967 22.1967i 0.976212 0.976212i
\(518\) 0 0
\(519\) 32.0820i 1.40824i
\(520\) 1.13415 6.94238i 0.0497358 0.304444i
\(521\) −13.4493 7.76498i −0.589226 0.340190i 0.175565 0.984468i \(-0.443825\pi\)
−0.764792 + 0.644278i \(0.777158\pi\)
\(522\) −36.7387 + 22.8743i −1.60801 + 1.00118i
\(523\) −10.3555 2.77474i −0.452814 0.121331i 0.0252020 0.999682i \(-0.491977\pi\)
−0.478016 + 0.878351i \(0.658644\pi\)
\(524\) −23.0085 4.54974i −1.00513 0.198756i
\(525\) 0 0
\(526\) −18.4422 + 5.60571i −0.804117 + 0.244421i
\(527\) 2.17349 + 3.76460i 0.0946787 + 0.163988i
\(528\) 24.0907 + 31.2496i 1.04841 + 1.35997i
\(529\) −10.7068 + 18.5448i −0.465514 + 0.806294i
\(530\) 6.55932 + 6.13654i 0.284918 + 0.266554i
\(531\) 12.3680 + 12.3680i 0.536725 + 0.536725i
\(532\) 0 0
\(533\) 3.83929 3.83929i 0.166298 0.166298i
\(534\) −1.50555 45.2114i −0.0651514 1.95649i
\(535\) −8.50955 4.91299i −0.367900 0.212407i
\(536\) 5.80704 + 2.61932i 0.250826 + 0.113138i
\(537\) 38.1452 22.0231i 1.64609 0.950368i
\(538\) 4.17217 7.81615i 0.179875 0.336978i
\(539\) 0 0
\(540\) 7.40423 + 11.0542i 0.318627 + 0.475699i
\(541\) 6.14630 22.9383i 0.264250 0.986194i −0.698458 0.715651i \(-0.746130\pi\)
0.962708 0.270543i \(-0.0872033\pi\)
\(542\) 17.4731 + 4.06378i 0.750533 + 0.174554i
\(543\) −16.2930 + 28.2202i −0.699198 + 1.21105i
\(544\) 2.30437 + 5.04800i 0.0987990 + 0.216431i
\(545\) −7.90771 −0.338729
\(546\) 0 0
\(547\) −28.9159 28.9159i −1.23636 1.23636i −0.961480 0.274875i \(-0.911363\pi\)
−0.274875 0.961480i \(-0.588637\pi\)
\(548\) 9.15418 18.6156i 0.391047 0.795221i
\(549\) 6.45868 + 24.1041i 0.275650 + 1.02874i
\(550\) 11.0382 + 17.7286i 0.470671 + 0.755952i
\(551\) −28.9360 + 16.7062i −1.23271 + 0.711708i
\(552\) 11.1071 1.11290i 0.472752 0.0473683i
\(553\) 0 0
\(554\) −30.1429 16.0899i −1.28065 0.683595i
\(555\) 1.53528 + 0.411377i 0.0651691 + 0.0174620i
\(556\) 10.2874 + 9.00135i 0.436284 + 0.381742i
\(557\) −16.2223 + 4.34676i −0.687362 + 0.184178i −0.585563 0.810627i \(-0.699127\pi\)
−0.101799 + 0.994805i \(0.532460\pi\)
\(558\) 31.2050 + 29.1937i 1.32101 + 1.23587i
\(559\) −6.11449 −0.258616
\(560\) 0 0
\(561\) 9.67648 0.408541
\(562\) 13.2838 + 12.4276i 0.560342 + 0.524225i
\(563\) 3.44149 0.922146i 0.145042 0.0388638i −0.185568 0.982631i \(-0.559412\pi\)
0.330609 + 0.943768i \(0.392746\pi\)
\(564\) 41.1500 47.0293i 1.73273 1.98029i
\(565\) 2.69546 + 0.722246i 0.113399 + 0.0303851i
\(566\) 1.55104 + 0.827928i 0.0651952 + 0.0348004i
\(567\) 0 0
\(568\) −1.67359 + 2.04632i −0.0702224 + 0.0858615i
\(569\) 1.64887 0.951974i 0.0691241 0.0399088i −0.465040 0.885290i \(-0.653960\pi\)
0.534164 + 0.845381i \(0.320627\pi\)
\(570\) 9.69448 + 15.5704i 0.406057 + 0.652174i
\(571\) 0.712086 + 2.65754i 0.0297999 + 0.111215i 0.979224 0.202782i \(-0.0649984\pi\)
−0.949424 + 0.313997i \(0.898332\pi\)
\(572\) −25.2745 12.4287i −1.05678 0.519669i
\(573\) 7.85872 + 7.85872i 0.328303 + 0.328303i
\(574\) 0 0
\(575\) 5.90824 0.246390
\(576\) 36.1050 + 40.8905i 1.50438 + 1.70377i
\(577\) 0.135023 0.233867i 0.00562108 0.00973599i −0.863201 0.504860i \(-0.831544\pi\)
0.868822 + 0.495124i \(0.164877\pi\)
\(578\) −22.0912 5.13783i −0.918872 0.213706i
\(579\) 2.42809 9.06176i 0.100908 0.376594i
\(580\) 4.14617 2.77714i 0.172160 0.115315i
\(581\) 0 0
\(582\) −6.33711 + 11.8720i −0.262682 + 0.492109i
\(583\) 31.1460 17.9821i 1.28994 0.744744i
\(584\) −0.711068 1.87963i −0.0294242 0.0777795i
\(585\) −14.6862 8.47911i −0.607202 0.350568i
\(586\) −1.19771 35.9671i −0.0494770 1.48579i
\(587\) −22.4556 + 22.4556i −0.926842 + 0.926842i −0.997501 0.0706582i \(-0.977490\pi\)
0.0706582 + 0.997501i \(0.477490\pi\)
\(588\) 0 0
\(589\) 23.3282 + 23.3282i 0.961221 + 0.961221i
\(590\) −1.47281 1.37789i −0.0606348 0.0567267i
\(591\) −7.87338 + 13.6371i −0.323867 + 0.560955i
\(592\) 3.61933 + 0.468205i 0.148754 + 0.0192431i
\(593\) 18.0313 + 31.2311i 0.740456 + 1.28251i 0.952288 + 0.305201i \(0.0987238\pi\)
−0.211832 + 0.977306i \(0.567943\pi\)
\(594\) 50.9688 15.4926i 2.09127 0.635667i
\(595\) 0 0
\(596\) −0.954964 + 4.82934i −0.0391168 + 0.197817i
\(597\) −5.45136 1.46069i −0.223109 0.0597820i
\(598\) −6.76413 + 4.21149i −0.276606 + 0.172221i
\(599\) −9.29172 5.36458i −0.379649 0.219191i 0.298016 0.954561i \(-0.403675\pi\)
−0.677666 + 0.735370i \(0.737008\pi\)
\(600\) 24.2733 + 33.7528i 0.990952 + 1.37795i
\(601\) 36.0677i 1.47123i 0.677399 + 0.735616i \(0.263107\pi\)
−0.677399 + 0.735616i \(0.736893\pi\)
\(602\) 0 0
\(603\) 10.8594 10.8594i 0.442230 0.442230i
\(604\) −18.3687 + 37.3540i −0.747412 + 1.51991i
\(605\) 0.585153 0.156791i 0.0237899 0.00637448i
\(606\) −62.0460 14.4303i −2.52045 0.586190i
\(607\) −3.49308 6.05020i −0.141780 0.245570i 0.786387 0.617734i \(-0.211949\pi\)
−0.928167 + 0.372164i \(0.878616\pi\)
\(608\) 26.8086 + 32.4795i 1.08723 + 1.31722i
\(609\) 0 0
\(610\) −0.836836 2.75310i −0.0338825 0.111470i
\(611\) −11.5450 + 43.0864i −0.467059 + 1.74309i
\(612\) 13.3479 0.889959i 0.539555 0.0359745i
\(613\) −8.54889 31.9049i −0.345286 1.28863i −0.892277 0.451488i \(-0.850893\pi\)
0.546991 0.837138i \(-0.315773\pi\)
\(614\) 3.49780 0.116477i 0.141160 0.00470064i
\(615\) 2.11447i 0.0852635i
\(616\) 0 0
\(617\) 41.5107i 1.67116i 0.549370 + 0.835579i \(0.314868\pi\)
−0.549370 + 0.835579i \(0.685132\pi\)
\(618\) −0.893048 26.8181i −0.0359237 1.07878i
\(619\) −7.08429 26.4389i −0.284742 1.06267i −0.949028 0.315192i \(-0.897931\pi\)
0.664286 0.747478i \(-0.268736\pi\)
\(620\) −3.70826 3.24468i −0.148927 0.130309i
\(621\) 3.90060 14.5572i 0.156526 0.584162i
\(622\) −23.5827 + 7.16822i −0.945579 + 0.287420i
\(623\) 0 0
\(624\) −51.8491 21.3399i −2.07563 0.854282i
\(625\) 10.2296 + 17.7181i 0.409182 + 0.708724i
\(626\) 9.07993 39.0411i 0.362907 1.56040i
\(627\) 70.9365 19.0074i 2.83293 0.759081i
\(628\) −9.25329 27.1588i −0.369246 1.08375i
\(629\) 0.632856 0.632856i 0.0252336 0.0252336i
\(630\) 0 0
\(631\) 2.56032i 0.101925i −0.998701 0.0509624i \(-0.983771\pi\)
0.998701 0.0509624i \(-0.0162289\pi\)
\(632\) 5.41045 33.1185i 0.215216 1.31738i
\(633\) 57.9576 + 33.4618i 2.30361 + 1.32999i
\(634\) 8.71464 + 13.9967i 0.346102 + 0.555880i
\(635\) −10.4112 2.78966i −0.413154 0.110704i
\(636\) 59.4842 39.8430i 2.35870 1.57988i
\(637\) 0 0
\(638\) −5.81087 19.1171i −0.230055 0.756854i
\(639\) 3.18646 + 5.51912i 0.126055 + 0.218333i
\(640\) −4.31786 4.57387i −0.170678 0.180798i
\(641\) 0.327094 0.566544i 0.0129195 0.0223771i −0.859493 0.511147i \(-0.829221\pi\)
0.872413 + 0.488770i \(0.162554\pi\)
\(642\) −53.5065 + 57.1928i −2.11173 + 2.25722i
\(643\) 3.21708 + 3.21708i 0.126869 + 0.126869i 0.767690 0.640821i \(-0.221406\pi\)
−0.640821 + 0.767690i \(0.721406\pi\)
\(644\) 0 0
\(645\) −1.68376 + 1.68376i −0.0662980 + 0.0662980i
\(646\) 10.3223 0.343735i 0.406126 0.0135241i
\(647\) 34.1274 + 19.7035i 1.34169 + 0.774623i 0.987055 0.160382i \(-0.0512728\pi\)
0.354632 + 0.935006i \(0.384606\pi\)
\(648\) 45.0730 17.0512i 1.77063 0.669835i
\(649\) −6.99345 + 4.03767i −0.274517 + 0.158493i
\(650\) −26.1799 13.9745i −1.02686 0.548126i
\(651\) 0 0
\(652\) 32.9861 + 6.52273i 1.29183 + 0.255450i
\(653\) 9.30692 34.7339i 0.364208 1.35924i −0.504284 0.863538i \(-0.668243\pi\)
0.868491 0.495704i \(-0.165090\pi\)
\(654\) −14.2780 + 61.3912i −0.558314 + 2.40059i
\(655\) 3.25989 5.64629i 0.127374 0.220619i
\(656\) −0.644542 4.81202i −0.0251651 0.187878i
\(657\) −4.84472 −0.189010
\(658\) 0 0
\(659\) 31.8006 + 31.8006i 1.23877 + 1.23877i 0.960502 + 0.278272i \(0.0897616\pi\)
0.278272 + 0.960502i \(0.410238\pi\)
\(660\) −10.3824 + 3.53740i −0.404135 + 0.137693i
\(661\) −1.99669 7.45175i −0.0776622 0.289839i 0.916162 0.400809i \(-0.131271\pi\)
−0.993824 + 0.110970i \(0.964604\pi\)
\(662\) 0.399770 0.248905i 0.0155375 0.00967397i
\(663\) −11.9080 + 6.87511i −0.462470 + 0.267007i
\(664\) −2.70174 26.9643i −0.104848 1.04642i
\(665\) 0 0
\(666\) 4.14299 7.76150i 0.160538 0.300752i
\(667\) −5.46006 1.46302i −0.211414 0.0566483i
\(668\) 2.21245 0.147514i 0.0856023 0.00570747i
\(669\) −21.5276 + 5.76831i −0.832307 + 0.223016i
\(670\) −1.20982 + 1.29317i −0.0467395 + 0.0499596i
\(671\) −11.5211 −0.444768
\(672\) 0 0
\(673\) −28.3929 −1.09446 −0.547232 0.836981i \(-0.684319\pi\)
−0.547232 + 0.836981i \(0.684319\pi\)
\(674\) −8.90899 + 9.52277i −0.343161 + 0.366803i
\(675\) 54.2168 14.5274i 2.08681 0.559158i
\(676\) 13.9914 0.932865i 0.538129 0.0358794i
\(677\) −10.3630 2.77675i −0.398281 0.106719i 0.0541182 0.998535i \(-0.482765\pi\)
−0.452400 + 0.891815i \(0.649432\pi\)
\(678\) 10.4740 19.6220i 0.402251 0.753579i
\(679\) 0 0
\(680\) −1.53486 + 0.153788i −0.0588592 + 0.00589752i
\(681\) −46.6999 + 26.9622i −1.78954 + 1.03319i
\(682\) −16.7479 + 10.4276i −0.641309 + 0.399292i
\(683\) −3.89792 14.5472i −0.149150 0.556634i −0.999536 0.0304747i \(-0.990298\pi\)
0.850386 0.526160i \(-0.176369\pi\)
\(684\) 96.1024 32.7431i 3.67457 1.25196i
\(685\) 4.07763 + 4.07763i 0.155798 + 0.155798i
\(686\) 0 0
\(687\) −2.75404 −0.105073
\(688\) −3.31859 + 4.34509i −0.126520 + 0.165655i
\(689\) −25.5525 + 44.2582i −0.973473 + 1.68610i
\(690\) −0.702926 + 3.02238i −0.0267599 + 0.115060i
\(691\) 0.482439 1.80049i 0.0183529 0.0684938i −0.956142 0.292903i \(-0.905379\pi\)
0.974495 + 0.224409i \(0.0720453\pi\)
\(692\) 20.0880 + 3.97225i 0.763631 + 0.151002i
\(693\) 0 0
\(694\) 14.1630 + 7.56003i 0.537620 + 0.286975i
\(695\) −3.29078 + 1.89994i −0.124827 + 0.0720686i
\(696\) −14.0740 37.2030i −0.533474 1.41018i
\(697\) −1.03111 0.595314i −0.0390562 0.0225491i
\(698\) −23.1630 + 0.771332i −0.876733 + 0.0291954i
\(699\) −10.7614 + 10.7614i −0.407033 + 0.407033i
\(700\) 0 0
\(701\) 5.77893 + 5.77893i 0.218267 + 0.218267i 0.807768 0.589501i \(-0.200675\pi\)
−0.589501 + 0.807768i \(0.700675\pi\)
\(702\) −51.7156 + 55.2785i −1.95188 + 2.08635i
\(703\) 3.39624 5.88245i 0.128091 0.221861i
\(704\) −22.5496 + 11.2151i −0.849871 + 0.422685i
\(705\) 8.68562 + 15.0439i 0.327119 + 0.566588i
\(706\) −7.79308 25.6384i −0.293296 0.964913i
\(707\) 0 0
\(708\) −13.3565 + 8.94626i −0.501966 + 0.336221i
\(709\) 37.6192 + 10.0800i 1.41282 + 0.378564i 0.882931 0.469503i \(-0.155567\pi\)
0.529889 + 0.848067i \(0.322233\pi\)
\(710\) −0.388405 0.623823i −0.0145766 0.0234117i
\(711\) −70.0606 40.4495i −2.62748 1.51697i
\(712\) 28.4953 + 4.65517i 1.06791 + 0.174460i
\(713\) 5.58138i 0.209024i
\(714\) 0 0
\(715\) 5.53621 5.53621i 0.207043 0.207043i
\(716\) 9.06673 + 26.6112i 0.338840 + 0.994509i
\(717\) −14.8621 + 3.98229i −0.555035 + 0.148721i
\(718\) −1.13462 + 4.87854i −0.0423437 + 0.182066i
\(719\) 1.89904 + 3.28924i 0.0708223 + 0.122668i 0.899262 0.437411i \(-0.144104\pi\)
−0.828440 + 0.560078i \(0.810771\pi\)
\(720\) −13.9963 + 5.83441i −0.521610 + 0.217436i
\(721\) 0 0
\(722\) 49.2870 14.9814i 1.83427 0.557548i
\(723\) 8.80677 32.8673i 0.327527 1.22235i
\(724\) −15.6527 13.6959i −0.581727 0.509003i
\(725\) −5.44885 20.3354i −0.202365 0.755238i
\(726\) −0.160704 4.82592i −0.00596428 0.179107i
\(727\) 25.5053i 0.945937i −0.881079 0.472969i \(-0.843182\pi\)
0.881079 0.472969i \(-0.156818\pi\)
\(728\) 0 0
\(729\) 3.69376i 0.136806i
\(730\) 0.558331 0.0185925i 0.0206647 0.000688140i
\(731\) 0.347030 + 1.29513i 0.0128354 + 0.0479023i
\(732\) −22.8845 + 1.52581i −0.845837 + 0.0563956i
\(733\) −10.6201 + 39.6348i −0.392263 + 1.46395i 0.434129 + 0.900851i \(0.357056\pi\)
−0.826392 + 0.563095i \(0.809611\pi\)
\(734\) −4.60123 15.1376i −0.169835 0.558737i
\(735\) 0 0
\(736\) −0.678397 + 7.09249i −0.0250060 + 0.261433i
\(737\) 3.54519 + 6.14045i 0.130589 + 0.226186i
\(738\) −11.3999 2.65133i −0.419638 0.0975967i
\(739\) −2.28087 + 0.611156i −0.0839030 + 0.0224817i −0.300526 0.953774i \(-0.597162\pi\)
0.216623 + 0.976255i \(0.430496\pi\)
\(740\) −0.447674 + 0.910375i −0.0164568 + 0.0334660i
\(741\) −73.7909 + 73.7909i −2.71077 + 2.71077i
\(742\) 0 0
\(743\) 24.1373i 0.885513i 0.896642 + 0.442756i \(0.145999\pi\)
−0.896642 + 0.442756i \(0.854001\pi\)
\(744\) −31.8855 + 22.9304i −1.16898 + 0.840670i
\(745\) −1.18512 0.684231i −0.0434196 0.0250683i
\(746\) 23.4419 14.5954i 0.858269 0.534376i
\(747\) −63.1036 16.9086i −2.30884 0.618652i
\(748\) −1.19810 + 6.05889i −0.0438068 + 0.221535i
\(749\) 0 0
\(750\) −22.8434 + 6.94353i −0.834125 + 0.253542i
\(751\) −8.83513 15.3029i −0.322398 0.558410i 0.658584 0.752507i \(-0.271156\pi\)
−0.980982 + 0.194097i \(0.937822\pi\)
\(752\) 24.3522 + 31.5888i 0.888033 + 1.15193i
\(753\) −18.1358 + 31.4122i −0.660907 + 1.14472i
\(754\) 20.7336 + 19.3972i 0.755073 + 0.706406i
\(755\) −8.18214 8.18214i −0.297779 0.297779i
\(756\) 0 0
\(757\) −14.3436 + 14.3436i −0.521327 + 0.521327i −0.917972 0.396645i \(-0.870174\pi\)
0.396645 + 0.917972i \(0.370174\pi\)
\(758\) −0.731367 21.9628i −0.0265645 0.797727i
\(759\) 10.7598 + 6.21215i 0.390554 + 0.225487i
\(760\) −10.9497 + 4.14230i −0.397187 + 0.150257i
\(761\) 11.6399 6.72028i 0.421945 0.243610i −0.273964 0.961740i \(-0.588335\pi\)
0.695909 + 0.718130i \(0.255002\pi\)
\(762\) −40.4556 + 75.7897i −1.46555 + 2.74557i
\(763\) 0 0
\(764\) −5.89373 + 3.94767i −0.213228 + 0.142822i
\(765\) −0.962469 + 3.59198i −0.0347982 + 0.129868i
\(766\) −6.66610 1.55036i −0.240856 0.0560168i
\(767\) 5.73750 9.93765i 0.207169 0.358828i
\(768\) −43.3053 + 25.2631i −1.56265 + 0.911602i
\(769\) −42.7134 −1.54029 −0.770143 0.637871i \(-0.779815\pi\)
−0.770143 + 0.637871i \(0.779815\pi\)
\(770\) 0 0
\(771\) 45.6722 + 45.6722i 1.64484 + 1.64484i
\(772\) 5.37335 + 2.64233i 0.193391 + 0.0950994i
\(773\) 6.45078 + 24.0746i 0.232018 + 0.865905i 0.979470 + 0.201589i \(0.0646104\pi\)
−0.747452 + 0.664316i \(0.768723\pi\)
\(774\) 6.96657 + 11.1891i 0.250408 + 0.402184i
\(775\) −18.0023 + 10.3936i −0.646661 + 0.373350i
\(776\) −6.64895 5.43789i −0.238683 0.195209i
\(777\) 0 0
\(778\) −22.0206 11.7543i −0.789475 0.421412i
\(779\) −8.72827 2.33873i −0.312723 0.0837938i
\(780\) 10.2635 11.7298i 0.367490 0.419996i
\(781\) −2.84204 + 0.761522i −0.101696 + 0.0272494i
\(782\) 1.27595 + 1.19371i 0.0456279 + 0.0426870i
\(783\) −53.7014 −1.91913
\(784\) 0 0
\(785\) 7.97582 0.284669
\(786\) −37.9488 35.5029i −1.35359 1.26635i
\(787\) −37.5097 + 10.0507i −1.33708 + 0.358268i −0.855349 0.518053i \(-0.826657\pi\)
−0.481727 + 0.876321i \(0.659990\pi\)
\(788\) −7.56396 6.61836i −0.269455 0.235769i
\(789\) −41.2530 11.0537i −1.46865 0.393523i
\(790\) 8.22938 + 4.39274i 0.292788 + 0.156287i
\(791\) 0 0
\(792\) 6.05303 + 60.4113i 0.215085 + 2.14662i
\(793\) 14.1781 8.18572i 0.503478 0.290683i
\(794\) −12.4254 19.9565i −0.440959 0.708231i
\(795\) 5.15103 + 19.2239i 0.182688 + 0.681802i
\(796\) 1.58957 3.23249i 0.0563406 0.114573i
\(797\) 37.2933 + 37.2933i 1.32100 + 1.32100i 0.912971 + 0.408024i \(0.133782\pi\)
0.408024 + 0.912971i \(0.366218\pi\)
\(798\) 0 0
\(799\) 9.78152 0.346045
\(800\) −24.1395 + 11.0195i −0.853462 + 0.389598i
\(801\) 34.8029 60.2804i 1.22970 2.12990i
\(802\) −35.2384 8.19552i −1.24431 0.289394i
\(803\) 0.578911 2.16053i 0.0204293 0.0762433i
\(804\) 7.85507 + 11.7273i 0.277027 + 0.413592i
\(805\) 0 0
\(806\) 13.2014 24.7316i 0.465001 0.871134i
\(807\) 17.0010 9.81552i 0.598463 0.345523i
\(808\) 16.7177 37.0632i 0.588127 1.30388i
\(809\) 38.3756 + 22.1562i 1.34922 + 0.778970i 0.988138 0.153566i \(-0.0490758\pi\)
0.361077 + 0.932536i \(0.382409\pi\)
\(810\) 0.445844 + 13.3886i 0.0156654 + 0.470428i
\(811\) 9.44442 9.44442i 0.331639 0.331639i −0.521570 0.853209i \(-0.674653\pi\)
0.853209 + 0.521570i \(0.174653\pi\)
\(812\) 0 0
\(813\) 28.1063 + 28.1063i 0.985731 + 0.985731i
\(814\) 2.96622 + 2.77503i 0.103966 + 0.0972649i
\(815\) −4.67354 + 8.09480i −0.163707 + 0.283549i
\(816\) −1.57738 + 12.1935i −0.0552194 + 0.426858i
\(817\) 5.08802 + 8.81271i 0.178007 + 0.308318i
\(818\) 25.9963 7.90187i 0.908939 0.276283i
\(819\) 0 0
\(820\) 1.32396 + 0.261803i 0.0462348 + 0.00914257i
\(821\) −48.2759 12.9355i −1.68484 0.451451i −0.715789 0.698316i \(-0.753933\pi\)
−0.969050 + 0.246865i \(0.920600\pi\)
\(822\) 39.0190 24.2940i 1.36094 0.847352i
\(823\) 20.5366 + 11.8568i 0.715861 + 0.413302i 0.813227 0.581946i \(-0.197709\pi\)
−0.0973664 + 0.995249i \(0.531042\pi\)
\(824\) 16.9026 + 2.76132i 0.588831 + 0.0961950i
\(825\) 46.2729i 1.61102i
\(826\) 0 0
\(827\) 34.8453 34.8453i 1.21169 1.21169i 0.241218 0.970471i \(-0.422453\pi\)
0.970471 0.241218i \(-0.0775470\pi\)
\(828\) 15.4135 + 7.57952i 0.535655 + 0.263406i
\(829\) −16.3740 + 4.38741i −0.568694 + 0.152381i −0.531697 0.846934i \(-0.678446\pi\)
−0.0369962 + 0.999315i \(0.511779\pi\)
\(830\) 7.33728 + 1.70646i 0.254681 + 0.0592321i
\(831\) −37.8534 65.5641i −1.31312 2.27439i
\(832\) 19.7816 29.8229i 0.685805 1.03392i
\(833\) 0 0
\(834\) 8.80831 + 28.9784i 0.305007 + 1.00344i
\(835\) −0.159532 + 0.595383i −0.00552085 + 0.0206041i
\(836\) 3.11835 + 46.7700i 0.107851 + 1.61757i
\(837\) 13.7237 + 51.2175i 0.474360 + 1.77033i
\(838\) −22.5403 + 0.750596i −0.778642 + 0.0259289i
\(839\) 1.32175i 0.0456320i −0.999740 0.0228160i \(-0.992737\pi\)
0.999740 0.0228160i \(-0.00726318\pi\)
\(840\) 0 0
\(841\) 8.85792i 0.305445i
\(842\) 1.80409 + 54.1767i 0.0621732 + 1.86705i
\(843\) 10.4317 + 38.9318i 0.359288 + 1.34088i
\(844\) −28.1280 + 32.1468i −0.968206 + 1.10654i
\(845\) −1.00887 + 3.76516i −0.0347062 + 0.129525i
\(846\) 91.9989 27.9641i 3.16299 0.961426i
\(847\) 0 0
\(848\) 17.5825 + 42.1789i 0.603784 + 1.44843i
\(849\) 1.94780 + 3.37369i 0.0668483 + 0.115785i
\(850\) −1.47415 + 6.33840i −0.0505628 + 0.217405i
\(851\) 1.10999 0.297420i 0.0380498 0.0101954i
\(852\) −5.54433 + 1.88901i −0.189945 + 0.0647164i
\(853\) 33.7981 33.7981i 1.15722 1.15722i 0.172153 0.985070i \(-0.444928\pi\)
0.985070 0.172153i \(-0.0550725\pi\)
\(854\) 0 0
\(855\) 28.2227i 0.965196i
\(856\) −29.1861 40.5842i −0.997560 1.38714i
\(857\) 10.5676 + 6.10119i 0.360982 + 0.208413i 0.669511 0.742802i \(-0.266504\pi\)
−0.308530 + 0.951215i \(0.599837\pi\)
\(858\) −32.9841 52.9762i −1.12606 1.80858i
\(859\) 13.1420 + 3.52139i 0.448400 + 0.120148i 0.475951 0.879472i \(-0.342104\pi\)
−0.0275506 + 0.999620i \(0.508771\pi\)
\(860\) −0.845804 1.26276i −0.0288417 0.0430596i
\(861\) 0 0
\(862\) 6.07134 + 19.9740i 0.206791 + 0.680319i
\(863\) 24.2546 + 42.0102i 0.825636 + 1.43004i 0.901433 + 0.432920i \(0.142517\pi\)
−0.0757970 + 0.997123i \(0.524150\pi\)
\(864\) 11.2139 + 66.7522i 0.381506 + 2.27095i
\(865\) −2.84611 + 4.92961i −0.0967707 + 0.167612i
\(866\) 28.9904 30.9877i 0.985135 1.05301i
\(867\) −35.5348 35.5348i −1.20682 1.20682i
\(868\) 0 0
\(869\) 26.4104 26.4104i 0.895913 0.895913i
\(870\) 11.0509 0.367998i 0.374661 0.0124763i
\(871\) −8.72554 5.03769i −0.295654 0.170696i
\(872\) −36.6720 16.5413i −1.24187 0.560158i
\(873\) −17.9329 + 10.3536i −0.606936 + 0.350415i
\(874\) 11.6985 + 6.24454i 0.395709 + 0.211225i
\(875\) 0 0
\(876\) 0.863767 4.36815i 0.0291840 0.147586i
\(877\) −5.71771 + 21.3388i −0.193073 + 0.720560i 0.799684 + 0.600422i \(0.205001\pi\)
−0.992757 + 0.120138i \(0.961666\pi\)
\(878\) 10.8128 46.4921i 0.364916 1.56903i
\(879\) 39.8682 69.0538i 1.34472 2.32913i
\(880\) −0.929423 6.93888i −0.0313308 0.233910i
\(881\) 22.7269 0.765688 0.382844 0.923813i \(-0.374945\pi\)
0.382844 + 0.923813i \(0.374945\pi\)
\(882\) 0 0
\(883\) −30.2833 30.2833i −1.01912 1.01912i −0.999814 0.0193019i \(-0.993856\pi\)
−0.0193019 0.999814i \(-0.506144\pi\)
\(884\) −2.83042 8.30741i −0.0951973 0.279408i
\(885\) −1.15660 4.31650i −0.0388788 0.145098i
\(886\) 8.86290 5.51823i 0.297755 0.185389i
\(887\) 33.5292 19.3581i 1.12580 0.649980i 0.182924 0.983127i \(-0.441444\pi\)
0.942875 + 0.333147i \(0.108110\pi\)
\(888\) 6.25935 + 5.11925i 0.210050 + 0.171791i
\(889\) 0 0
\(890\) −3.77953 + 7.08059i −0.126690 + 0.237342i
\(891\) 51.8089 + 13.8822i 1.73566 + 0.465070i
\(892\) −0.946352 14.1936i −0.0316862 0.475238i
\(893\) 71.7065 19.2137i 2.39957 0.642962i
\(894\) −7.45184 + 7.96523i −0.249227 + 0.266397i
\(895\) −7.81501 −0.261227
\(896\) 0 0
\(897\) −17.6548 −0.589478
\(898\) 1.53626 1.64210i 0.0512656 0.0547975i
\(899\) 19.2104 5.14741i 0.640703 0.171676i
\(900\) 4.25578 + 63.8294i 0.141859 + 2.12765i
\(901\) 10.8247 + 2.90048i 0.360624 + 0.0966290i
\(902\) 2.54459 4.76705i 0.0847256 0.158725i
\(903\) 0 0
\(904\) 10.9894 + 8.98775i 0.365502 + 0.298928i
\(905\) 5.00704 2.89082i 0.166440 0.0960940i
\(906\) −78.2952 + 48.7483i −2.60119 + 1.61955i
\(907\) −9.32356 34.7960i −0.309584 1.15538i −0.928927 0.370262i \(-0.879268\pi\)
0.619344 0.785120i \(-0.287399\pi\)
\(908\) −11.1001 32.5792i −0.368369 1.08118i
\(909\) −69.3098 69.3098i −2.29886 2.29886i
\(910\) 0 0
\(911\) −52.6922 −1.74577 −0.872886 0.487924i \(-0.837754\pi\)
−0.872886 + 0.487924i \(0.837754\pi\)
\(912\) 12.3881 + 92.4867i 0.410209 + 3.06254i
\(913\) 15.0809 26.1209i 0.499106 0.864477i
\(914\) −0.688507 + 2.96038i −0.0227738 + 0.0979207i
\(915\) 1.65013 6.15836i 0.0545516 0.203589i
\(916\) 0.340992 1.72443i 0.0112667 0.0569768i
\(917\) 0 0
\(918\) 14.6439 + 7.81672i 0.483320 + 0.257990i
\(919\) 22.0937 12.7558i 0.728803 0.420775i −0.0891810 0.996015i \(-0.528425\pi\)
0.817984 + 0.575241i \(0.195092\pi\)
\(920\) −1.80542 0.814351i −0.0595228 0.0268484i
\(921\) 6.71547 + 3.87718i 0.221282 + 0.127757i
\(922\) 53.4516 1.77995i 1.76033 0.0586194i
\(923\) 2.95640 2.95640i 0.0973111 0.0973111i
\(924\) 0 0
\(925\) 3.02632 + 3.02632i 0.0995046 + 0.0995046i
\(926\) −15.7181 + 16.8010i −0.516530 + 0.552116i
\(927\) 20.6441 35.7566i 0.678041 1.17440i
\(928\) 25.0371 4.20607i 0.821883 0.138071i
\(929\) −24.5999 42.6083i −0.807097 1.39793i −0.914866 0.403757i \(-0.867704\pi\)
0.107770 0.994176i \(-0.465629\pi\)
\(930\) −3.17509 10.4457i −0.104115 0.342528i
\(931\) 0 0
\(932\) −5.40577 8.07062i −0.177072 0.264362i
\(933\) −52.7517 14.1348i −1.72701 0.462752i
\(934\) 18.9521 + 30.4392i 0.620130 + 0.996000i
\(935\) −1.48686 0.858436i −0.0486254 0.0280739i
\(936\) −50.3710 70.0424i −1.64643 2.28941i
\(937\) 44.3522i 1.44892i 0.689315 + 0.724462i \(0.257912\pi\)
−0.689315 + 0.724462i \(0.742088\pi\)
\(938\) 0 0
\(939\) 62.7995 62.7995i 2.04939 2.04939i
\(940\) −10.4951 + 3.57579i −0.342313 + 0.116630i
\(941\) −19.2167 + 5.14910i −0.626447 + 0.167856i −0.558057 0.829803i \(-0.688453\pi\)
−0.0683899 + 0.997659i \(0.521786\pi\)
\(942\) 14.4010 61.9200i 0.469209 2.01746i
\(943\) −0.764364 1.32392i −0.0248911 0.0431127i
\(944\) −3.94793 9.47077i −0.128494 0.308247i
\(945\) 0 0
\(946\) −5.82230 + 1.76975i −0.189299 + 0.0575397i
\(947\) −8.15611 + 30.4390i −0.265038 + 0.989136i 0.697189 + 0.716887i \(0.254434\pi\)
−0.962227 + 0.272248i \(0.912233\pi\)
\(948\) 48.9617 55.9571i 1.59020 1.81740i
\(949\) 0.822629 + 3.07009i 0.0267037 + 0.0996594i
\(950\) 1.64374 + 49.3613i 0.0533299 + 1.60149i
\(951\) 36.5323i 1.18464i
\(952\) 0 0
\(953\) 52.5006i 1.70066i −0.526250 0.850330i \(-0.676402\pi\)
0.526250 0.850330i \(-0.323598\pi\)
\(954\) 110.103 3.66645i 3.56471 0.118706i
\(955\) −0.510368 1.90472i −0.0165151 0.0616353i
\(956\) −0.653335 9.79890i −0.0211304 0.316919i
\(957\) 11.4583 42.7628i 0.370393 1.38233i
\(958\) 6.98613 + 22.9836i 0.225712 + 0.742566i
\(959\) 0 0
\(960\) −2.76508 13.6597i −0.0892426 0.440865i
\(961\) 5.68136 + 9.84041i 0.183270 + 0.317433i
\(962\) −5.62193 1.30751i −0.181258 0.0421559i
\(963\) −116.405 + 31.1906i −3.75110 + 1.00510i
\(964\) 19.4893 + 9.58380i 0.627709 + 0.308673i
\(965\) −1.17699 + 1.17699i −0.0378888 + 0.0378888i
\(966\) 0 0
\(967\) 22.7183i 0.730572i −0.930895 0.365286i \(-0.880971\pi\)
0.930895 0.365286i \(-0.119029\pi\)
\(968\) 3.04162 + 0.496899i 0.0977615 + 0.0159709i
\(969\) 19.8179 + 11.4419i 0.636644 + 0.367567i
\(970\) 2.02694 1.26202i 0.0650813 0.0405210i
\(971\) 11.6299 + 3.11622i 0.373221 + 0.100004i 0.440554 0.897726i \(-0.354782\pi\)
−0.0673325 + 0.997731i \(0.521449\pi\)
\(972\) 34.3174 + 6.78600i 1.10073 + 0.217661i
\(973\) 0 0
\(974\) −52.8166 + 16.0542i −1.69235 + 0.514411i
\(975\) −32.8768 56.9442i −1.05290 1.82367i
\(976\) 1.87808 14.5180i 0.0601158 0.464709i
\(977\) 18.8637 32.6729i 0.603503 1.04530i −0.388783 0.921329i \(-0.627104\pi\)
0.992286 0.123969i \(-0.0395622\pi\)
\(978\) 54.4053 + 50.8986i 1.73969 + 1.62756i
\(979\) 22.7236 + 22.7236i 0.726250 + 0.726250i
\(980\) 0 0
\(981\) −68.5784 + 68.5784i −2.18954 + 2.18954i
\(982\) −1.78941 53.7359i −0.0571025 1.71478i
\(983\) 39.1070 + 22.5785i 1.24732 + 0.720141i 0.970574 0.240802i \(-0.0774104\pi\)
0.276747 + 0.960943i \(0.410744\pi\)
\(984\) 4.42302 9.80584i 0.141001 0.312599i
\(985\) 2.41959 1.39695i 0.0770946 0.0445106i
\(986\) 2.93186 5.49256i 0.0933694 0.174919i
\(987\) 0 0
\(988\) −37.0674 55.3403i −1.17927 1.76061i
\(989\) −0.445575 + 1.66291i −0.0141685 + 0.0528775i
\(990\) −16.4386 3.82318i −0.522453 0.121509i
\(991\) 23.1140 40.0346i 0.734240 1.27174i −0.220815 0.975316i \(-0.570872\pi\)
0.955056 0.296426i \(-0.0957949\pi\)
\(992\) −10.4099 22.8041i −0.330514 0.724031i
\(993\) 1.04343 0.0331121
\(994\) 0 0
\(995\) 0.708054 + 0.708054i 0.0224468 + 0.0224468i
\(996\) 26.4961 53.8816i 0.839560 1.70730i
\(997\) −9.97267 37.2185i −0.315838 1.17872i −0.923207 0.384303i \(-0.874442\pi\)
0.607369 0.794419i \(-0.292225\pi\)
\(998\) 4.78830 + 7.69055i 0.151571 + 0.243440i
\(999\) 9.45447 5.45854i 0.299126 0.172701i
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 784.2.x.l.557.3 24
7.2 even 3 inner 784.2.x.l.765.6 24
7.3 odd 6 784.2.m.h.589.2 12
7.4 even 3 112.2.m.d.29.2 12
7.5 odd 6 784.2.x.m.765.6 24
7.6 odd 2 784.2.x.m.557.3 24
16.5 even 4 inner 784.2.x.l.165.6 24
28.11 odd 6 448.2.m.d.337.1 12
56.11 odd 6 896.2.m.h.673.6 12
56.53 even 6 896.2.m.g.673.1 12
112.5 odd 12 784.2.x.m.373.3 24
112.11 odd 12 448.2.m.d.113.1 12
112.37 even 12 inner 784.2.x.l.373.3 24
112.53 even 12 112.2.m.d.85.2 yes 12
112.67 odd 12 896.2.m.h.225.6 12
112.69 odd 4 784.2.x.m.165.6 24
112.101 odd 12 784.2.m.h.197.2 12
112.109 even 12 896.2.m.g.225.1 12
224.11 odd 24 7168.2.a.bi.1.1 12
224.53 even 24 7168.2.a.bj.1.12 12
224.123 odd 24 7168.2.a.bi.1.12 12
224.165 even 24 7168.2.a.bj.1.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.d.29.2 12 7.4 even 3
112.2.m.d.85.2 yes 12 112.53 even 12
448.2.m.d.113.1 12 112.11 odd 12
448.2.m.d.337.1 12 28.11 odd 6
784.2.m.h.197.2 12 112.101 odd 12
784.2.m.h.589.2 12 7.3 odd 6
784.2.x.l.165.6 24 16.5 even 4 inner
784.2.x.l.373.3 24 112.37 even 12 inner
784.2.x.l.557.3 24 1.1 even 1 trivial
784.2.x.l.765.6 24 7.2 even 3 inner
784.2.x.m.165.6 24 112.69 odd 4
784.2.x.m.373.3 24 112.5 odd 12
784.2.x.m.557.3 24 7.6 odd 2
784.2.x.m.765.6 24 7.5 odd 6
896.2.m.g.225.1 12 112.109 even 12
896.2.m.g.673.1 12 56.53 even 6
896.2.m.h.225.6 12 112.67 odd 12
896.2.m.h.673.6 12 56.11 odd 6
7168.2.a.bi.1.1 12 224.11 odd 24
7168.2.a.bi.1.12 12 224.123 odd 24
7168.2.a.bj.1.1 12 224.165 even 24
7168.2.a.bj.1.12 12 224.53 even 24