Properties

Label 112.2.m.d.85.3
Level $112$
Weight $2$
Character 112.85
Analytic conductor $0.894$
Analytic rank $0$
Dimension $12$
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] = [112,2,Mod(29,112)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(112, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("112.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.m (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.894324502638\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.20138089353117696.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 85.3
Root \(-1.40471 + 0.163666i\) of defining polynomial
Character \(\chi\) \(=\) 112.85
Dual form 112.2.m.d.29.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.163666 - 1.40471i) q^{2} +(-2.05500 + 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(2.72766 + 2.72766i) q^{5} +(2.55034 + 3.22301i) q^{6} +1.00000i q^{7} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +O(q^{10})\) \(q+(0.163666 - 1.40471i) q^{2} +(-2.05500 + 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(2.72766 + 2.72766i) q^{5} +(2.55034 + 3.22301i) q^{6} +1.00000i q^{7} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +(4.27801 - 3.38515i) q^{10} +(0.919616 + 0.919616i) q^{11} +(4.94480 - 3.05500i) q^{12} +(-1.12607 + 1.12607i) q^{13} +(1.40471 + 0.163666i) q^{14} -11.2107 q^{15} +(3.57715 + 1.78996i) q^{16} -1.50885 q^{17} +(-7.65008 - 0.891330i) q^{18} +(1.46271 - 1.46271i) q^{19} +(-4.05500 - 6.56340i) q^{20} +(-2.05500 - 2.05500i) q^{21} +(1.44230 - 1.14128i) q^{22} -4.77031i q^{23} +(-3.48209 - 7.44602i) q^{24} +9.88030i q^{25} +(1.39751 + 1.76611i) q^{26} +(5.02656 + 5.02656i) q^{27} +(0.459808 - 1.94643i) q^{28} +(4.10069 - 4.10069i) q^{29} +(-1.83481 + 15.7478i) q^{30} +4.10999 q^{31} +(3.09984 - 4.73191i) q^{32} -3.77961 q^{33} +(-0.246948 + 2.11950i) q^{34} +(-2.72766 + 2.72766i) q^{35} +(-2.50412 + 10.6003i) q^{36} +(-1.65467 - 1.65467i) q^{37} +(-1.81529 - 2.29409i) q^{38} -4.62815i q^{39} +(-9.88334 + 4.62189i) q^{40} -7.45533i q^{41} +(-3.22301 + 2.55034i) q^{42} +(5.68992 + 5.68992i) q^{43} +(-1.36712 - 2.21281i) q^{44} +(14.8549 - 14.8549i) q^{45} +(-6.70090 - 0.780738i) q^{46} +3.59748 q^{47} +(-11.0294 + 3.67267i) q^{48} -1.00000 q^{49} +(13.8790 + 1.61707i) q^{50} +(3.10069 - 3.10069i) q^{51} +(2.70960 - 1.67404i) q^{52} +(-0.675714 - 0.675714i) q^{53} +(7.88355 - 6.23819i) q^{54} +5.01680i q^{55} +(-2.65891 - 0.964462i) q^{56} +6.01174i q^{57} +(-5.08913 - 6.43142i) q^{58} +(1.13843 + 1.13843i) q^{59} +(21.8208 + 5.15476i) q^{60} +(-3.21881 + 3.21881i) q^{61} +(0.672667 - 5.77335i) q^{62} +5.44602 q^{63} +(-6.13963 - 5.12884i) q^{64} -6.14310 q^{65} +(-0.618595 + 5.30926i) q^{66} +(-1.52640 + 1.52640i) q^{67} +(2.93687 + 0.693782i) q^{68} +(9.80296 + 9.80296i) q^{69} +(3.38515 + 4.27801i) q^{70} -13.8202i q^{71} +(14.4805 + 5.25248i) q^{72} +14.4749i q^{73} +(-2.59514 + 2.05351i) q^{74} +(-20.3040 - 20.3040i) q^{75} +(-3.51963 + 2.17450i) q^{76} +(-0.919616 + 0.919616i) q^{77} +(-6.50122 - 0.757473i) q^{78} -1.77961 q^{79} +(4.87485 + 14.6397i) q^{80} -4.32107 q^{81} +(-10.4726 - 1.22019i) q^{82} +(-7.16133 + 7.16133i) q^{83} +(3.05500 + 4.94480i) q^{84} +(-4.11564 - 4.11564i) q^{85} +(8.92394 - 7.06145i) q^{86} +16.8538i q^{87} +(-3.33211 + 1.55824i) q^{88} +8.45899i q^{89} +(-18.4356 - 23.2981i) q^{90} +(-1.12607 - 1.12607i) q^{91} +(-2.19342 + 9.28505i) q^{92} +(-8.44602 + 8.44602i) q^{93} +(0.588786 - 5.05342i) q^{94} +7.97958 q^{95} +(3.35389 + 16.0942i) q^{96} +16.2227 q^{97} +(-0.163666 + 1.40471i) q^{98} +(5.00824 - 5.00824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8} - 4 q^{10} + 8 q^{12} - 24 q^{15} + 10 q^{16} - 8 q^{17} - 20 q^{20} + 4 q^{21} + 14 q^{22} - 8 q^{24} - 20 q^{26} + 4 q^{27} - 4 q^{29} - 28 q^{30} - 8 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 6 q^{72} - 38 q^{74} - 40 q^{75} + 48 q^{76} - 76 q^{78} + 24 q^{79} + 24 q^{80} - 44 q^{81} - 16 q^{82} - 20 q^{83} + 8 q^{84} - 8 q^{85} + 38 q^{86} - 14 q^{88} - 40 q^{90} + 32 q^{92} - 48 q^{93} - 24 q^{94} - 16 q^{96} + 48 q^{97} - 2 q^{98} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.163666 1.40471i 0.115730 0.993281i
\(3\) −2.05500 + 2.05500i −1.18645 + 1.18645i −0.208411 + 0.978041i \(0.566829\pi\)
−0.978041 + 0.208411i \(0.933171\pi\)
\(4\) −1.94643 0.459808i −0.973213 0.229904i
\(5\) 2.72766 + 2.72766i 1.21985 + 1.21985i 0.967685 + 0.252164i \(0.0811421\pi\)
0.252164 + 0.967685i \(0.418858\pi\)
\(6\) 2.55034 + 3.22301i 1.04117 + 1.31579i
\(7\) 1.00000i 0.377964i
\(8\) −0.964462 + 2.65891i −0.340989 + 0.940067i
\(9\) 5.44602i 1.81534i
\(10\) 4.27801 3.38515i 1.35282 1.07048i
\(11\) 0.919616 + 0.919616i 0.277275 + 0.277275i 0.832020 0.554746i \(-0.187184\pi\)
−0.554746 + 0.832020i \(0.687184\pi\)
\(12\) 4.94480 3.05500i 1.42744 0.881901i
\(13\) −1.12607 + 1.12607i −0.312316 + 0.312316i −0.845806 0.533490i \(-0.820880\pi\)
0.533490 + 0.845806i \(0.320880\pi\)
\(14\) 1.40471 + 0.163666i 0.375425 + 0.0437417i
\(15\) −11.2107 −2.89458
\(16\) 3.57715 + 1.78996i 0.894288 + 0.447491i
\(17\) −1.50885 −0.365950 −0.182975 0.983118i \(-0.558573\pi\)
−0.182975 + 0.983118i \(0.558573\pi\)
\(18\) −7.65008 0.891330i −1.80314 0.210088i
\(19\) 1.46271 1.46271i 0.335569 0.335569i −0.519127 0.854697i \(-0.673743\pi\)
0.854697 + 0.519127i \(0.173743\pi\)
\(20\) −4.05500 6.56340i −0.906725 1.46762i
\(21\) −2.05500 2.05500i −0.448437 0.448437i
\(22\) 1.44230 1.14128i 0.307500 0.243323i
\(23\) 4.77031i 0.994677i −0.867556 0.497339i \(-0.834311\pi\)
0.867556 0.497339i \(-0.165689\pi\)
\(24\) −3.48209 7.44602i −0.710779 1.51991i
\(25\) 9.88030i 1.97606i
\(26\) 1.39751 + 1.76611i 0.274074 + 0.346362i
\(27\) 5.02656 + 5.02656i 0.967362 + 0.967362i
\(28\) 0.459808 1.94643i 0.0868955 0.367840i
\(29\) 4.10069 4.10069i 0.761478 0.761478i −0.215111 0.976590i \(-0.569011\pi\)
0.976590 + 0.215111i \(0.0690115\pi\)
\(30\) −1.83481 + 15.7478i −0.334989 + 2.87514i
\(31\) 4.10999 0.738176 0.369088 0.929394i \(-0.379670\pi\)
0.369088 + 0.929394i \(0.379670\pi\)
\(32\) 3.09984 4.73191i 0.547980 0.836492i
\(33\) −3.77961 −0.657946
\(34\) −0.246948 + 2.11950i −0.0423513 + 0.363491i
\(35\) −2.72766 + 2.72766i −0.461059 + 0.461059i
\(36\) −2.50412 + 10.6003i −0.417354 + 1.76671i
\(37\) −1.65467 1.65467i −0.272025 0.272025i 0.557890 0.829915i \(-0.311611\pi\)
−0.829915 + 0.557890i \(0.811611\pi\)
\(38\) −1.81529 2.29409i −0.294479 0.372150i
\(39\) 4.62815i 0.741097i
\(40\) −9.88334 + 4.62189i −1.56269 + 0.730785i
\(41\) 7.45533i 1.16433i −0.813072 0.582163i \(-0.802206\pi\)
0.813072 0.582163i \(-0.197794\pi\)
\(42\) −3.22301 + 2.55034i −0.497321 + 0.393526i
\(43\) 5.68992 + 5.68992i 0.867705 + 0.867705i 0.992218 0.124513i \(-0.0397369\pi\)
−0.124513 + 0.992218i \(0.539737\pi\)
\(44\) −1.36712 2.21281i −0.206101 0.333594i
\(45\) 14.8549 14.8549i 2.21444 2.21444i
\(46\) −6.70090 0.780738i −0.987994 0.115114i
\(47\) 3.59748 0.524747 0.262373 0.964966i \(-0.415495\pi\)
0.262373 + 0.964966i \(0.415495\pi\)
\(48\) −11.0294 + 3.67267i −1.59196 + 0.530104i
\(49\) −1.00000 −0.142857
\(50\) 13.8790 + 1.61707i 1.96278 + 0.228689i
\(51\) 3.10069 3.10069i 0.434183 0.434183i
\(52\) 2.70960 1.67404i 0.375753 0.232148i
\(53\) −0.675714 0.675714i −0.0928165 0.0928165i 0.659174 0.751990i \(-0.270906\pi\)
−0.751990 + 0.659174i \(0.770906\pi\)
\(54\) 7.88355 6.23819i 1.07281 0.848910i
\(55\) 5.01680i 0.676466i
\(56\) −2.65891 0.964462i −0.355312 0.128882i
\(57\) 6.01174i 0.796275i
\(58\) −5.08913 6.43142i −0.668236 0.844487i
\(59\) 1.13843 + 1.13843i 0.148211 + 0.148211i 0.777318 0.629108i \(-0.216580\pi\)
−0.629108 + 0.777318i \(0.716580\pi\)
\(60\) 21.8208 + 5.15476i 2.81705 + 0.665476i
\(61\) −3.21881 + 3.21881i −0.412127 + 0.412127i −0.882479 0.470352i \(-0.844127\pi\)
0.470352 + 0.882479i \(0.344127\pi\)
\(62\) 0.672667 5.77335i 0.0854288 0.733216i
\(63\) 5.44602 0.686134
\(64\) −6.13963 5.12884i −0.767453 0.641105i
\(65\) −6.14310 −0.761957
\(66\) −0.618595 + 5.30926i −0.0761438 + 0.653525i
\(67\) −1.52640 + 1.52640i −0.186480 + 0.186480i −0.794172 0.607692i \(-0.792095\pi\)
0.607692 + 0.794172i \(0.292095\pi\)
\(68\) 2.93687 + 0.693782i 0.356148 + 0.0841334i
\(69\) 9.80296 + 9.80296i 1.18014 + 1.18014i
\(70\) 3.38515 + 4.27801i 0.404603 + 0.511320i
\(71\) 13.8202i 1.64016i −0.572251 0.820079i \(-0.693930\pi\)
0.572251 0.820079i \(-0.306070\pi\)
\(72\) 14.4805 + 5.25248i 1.70654 + 0.619010i
\(73\) 14.4749i 1.69416i 0.531468 + 0.847078i \(0.321641\pi\)
−0.531468 + 0.847078i \(0.678359\pi\)
\(74\) −2.59514 + 2.05351i −0.301679 + 0.238716i
\(75\) −20.3040 20.3040i −2.34450 2.34450i
\(76\) −3.51963 + 2.17450i −0.403729 + 0.249432i
\(77\) −0.919616 + 0.919616i −0.104800 + 0.104800i
\(78\) −6.50122 0.757473i −0.736118 0.0857669i
\(79\) −1.77961 −0.200222 −0.100111 0.994976i \(-0.531920\pi\)
−0.100111 + 0.994976i \(0.531920\pi\)
\(80\) 4.87485 + 14.6397i 0.545025 + 1.63677i
\(81\) −4.32107 −0.480119
\(82\) −10.4726 1.22019i −1.15650 0.134747i
\(83\) −7.16133 + 7.16133i −0.786058 + 0.786058i −0.980845 0.194787i \(-0.937598\pi\)
0.194787 + 0.980845i \(0.437598\pi\)
\(84\) 3.05500 + 4.94480i 0.333327 + 0.539522i
\(85\) −4.11564 4.11564i −0.446404 0.446404i
\(86\) 8.92394 7.06145i 0.962294 0.761455i
\(87\) 16.8538i 1.80692i
\(88\) −3.33211 + 1.55824i −0.355204 + 0.166109i
\(89\) 8.45899i 0.896651i 0.893870 + 0.448325i \(0.147979\pi\)
−0.893870 + 0.448325i \(0.852021\pi\)
\(90\) −18.4356 23.2981i −1.94328 2.45584i
\(91\) −1.12607 1.12607i −0.118045 0.118045i
\(92\) −2.19342 + 9.28505i −0.228680 + 0.968033i
\(93\) −8.44602 + 8.44602i −0.875811 + 0.875811i
\(94\) 0.588786 5.05342i 0.0607287 0.521221i
\(95\) 7.97958 0.818688
\(96\) 3.35389 + 16.0942i 0.342305 + 1.64261i
\(97\) 16.2227 1.64717 0.823585 0.567194i \(-0.191971\pi\)
0.823585 + 0.567194i \(0.191971\pi\)
\(98\) −0.163666 + 1.40471i −0.0165328 + 0.141897i
\(99\) 5.00824 5.00824i 0.503348 0.503348i
\(100\) 4.54304 19.2313i 0.454304 1.92313i
\(101\) −11.5664 11.5664i −1.15090 1.15090i −0.986372 0.164533i \(-0.947388\pi\)
−0.164533 0.986372i \(-0.552612\pi\)
\(102\) −3.84809 4.86304i −0.381018 0.481513i
\(103\) 17.1875i 1.69354i −0.531963 0.846768i \(-0.678545\pi\)
0.531963 0.846768i \(-0.321455\pi\)
\(104\) −1.90808 4.08018i −0.187102 0.400095i
\(105\) 11.2107i 1.09405i
\(106\) −1.05977 + 0.838591i −0.102934 + 0.0814512i
\(107\) 4.10143 + 4.10143i 0.396501 + 0.396501i 0.876997 0.480496i \(-0.159543\pi\)
−0.480496 + 0.876997i \(0.659543\pi\)
\(108\) −7.47258 12.0951i −0.719049 1.16385i
\(109\) −3.27351 + 3.27351i −0.313545 + 0.313545i −0.846281 0.532736i \(-0.821164\pi\)
0.532736 + 0.846281i \(0.321164\pi\)
\(110\) 7.04716 + 0.821082i 0.671920 + 0.0782871i
\(111\) 6.80066 0.645490
\(112\) −1.78996 + 3.57715i −0.169136 + 0.338009i
\(113\) −9.17193 −0.862822 −0.431411 0.902155i \(-0.641984\pi\)
−0.431411 + 0.902155i \(0.641984\pi\)
\(114\) 8.44476 + 0.983920i 0.790924 + 0.0921525i
\(115\) 13.0118 13.0118i 1.21336 1.21336i
\(116\) −9.86721 + 6.09616i −0.916147 + 0.566014i
\(117\) 6.13262 + 6.13262i 0.566961 + 0.566961i
\(118\) 1.78548 1.41284i 0.164367 0.130062i
\(119\) 1.50885i 0.138316i
\(120\) 10.8123 29.8082i 0.987021 2.72110i
\(121\) 9.30861i 0.846238i
\(122\) 3.99469 + 5.04831i 0.361662 + 0.457053i
\(123\) 15.3207 + 15.3207i 1.38142 + 1.38142i
\(124\) −7.99980 1.88981i −0.718403 0.169710i
\(125\) −13.3118 + 13.3118i −1.19064 + 1.19064i
\(126\) 0.891330 7.65008i 0.0794060 0.681524i
\(127\) −12.9787 −1.15167 −0.575835 0.817566i \(-0.695323\pi\)
−0.575835 + 0.817566i \(0.695323\pi\)
\(128\) −8.20939 + 7.78499i −0.725614 + 0.688102i
\(129\) −23.3855 −2.05898
\(130\) −1.00542 + 8.62928i −0.0881810 + 0.756838i
\(131\) −6.81965 + 6.81965i −0.595836 + 0.595836i −0.939202 0.343366i \(-0.888433\pi\)
0.343366 + 0.939202i \(0.388433\pi\)
\(132\) 7.35674 + 1.73790i 0.640322 + 0.151264i
\(133\) 1.46271 + 1.46271i 0.126833 + 0.126833i
\(134\) 1.89434 + 2.39398i 0.163646 + 0.206808i
\(135\) 27.4215i 2.36007i
\(136\) 1.45523 4.01190i 0.124785 0.344018i
\(137\) 22.6543i 1.93548i −0.251943 0.967742i \(-0.581069\pi\)
0.251943 0.967742i \(-0.418931\pi\)
\(138\) 15.3747 12.1659i 1.30878 1.03563i
\(139\) −6.64728 6.64728i −0.563815 0.563815i 0.366574 0.930389i \(-0.380531\pi\)
−0.930389 + 0.366574i \(0.880531\pi\)
\(140\) 6.56340 4.05500i 0.554708 0.342710i
\(141\) −7.39281 + 7.39281i −0.622587 + 0.622587i
\(142\) −19.4134 2.26190i −1.62914 0.189815i
\(143\) −2.07111 −0.173195
\(144\) 9.74818 19.4812i 0.812348 1.62344i
\(145\) 22.3706 1.85778
\(146\) 20.3330 + 2.36905i 1.68277 + 0.196064i
\(147\) 2.05500 2.05500i 0.169493 0.169493i
\(148\) 2.45986 + 3.98151i 0.202199 + 0.327278i
\(149\) 7.77031 + 7.77031i 0.636568 + 0.636568i 0.949707 0.313139i \(-0.101381\pi\)
−0.313139 + 0.949707i \(0.601381\pi\)
\(150\) −31.8443 + 25.1981i −2.60008 + 2.05742i
\(151\) 5.46829i 0.445004i 0.974932 + 0.222502i \(0.0714223\pi\)
−0.974932 + 0.222502i \(0.928578\pi\)
\(152\) 2.47850 + 5.29996i 0.201033 + 0.429883i
\(153\) 8.21724i 0.664324i
\(154\) 1.14128 + 1.44230i 0.0919673 + 0.116224i
\(155\) 11.2107 + 11.2107i 0.900463 + 0.900463i
\(156\) −2.12806 + 9.00836i −0.170381 + 0.721246i
\(157\) −5.61722 + 5.61722i −0.448303 + 0.448303i −0.894790 0.446487i \(-0.852675\pi\)
0.446487 + 0.894790i \(0.352675\pi\)
\(158\) −0.291263 + 2.49984i −0.0231716 + 0.198877i
\(159\) 2.77718 0.220245
\(160\) 21.3624 4.45173i 1.68885 0.351940i
\(161\) 4.77031 0.375953
\(162\) −0.707214 + 6.06986i −0.0555640 + 0.476893i
\(163\) −6.31758 + 6.31758i −0.494831 + 0.494831i −0.909824 0.414994i \(-0.863784\pi\)
0.414994 + 0.909824i \(0.363784\pi\)
\(164\) −3.42802 + 14.5112i −0.267683 + 1.13314i
\(165\) −10.3095 10.3095i −0.802595 0.802595i
\(166\) 8.88753 + 11.2317i 0.689806 + 0.871746i
\(167\) 11.8175i 0.914463i −0.889348 0.457231i \(-0.848841\pi\)
0.889348 0.457231i \(-0.151159\pi\)
\(168\) 7.44602 3.48209i 0.574473 0.268649i
\(169\) 10.4639i 0.804917i
\(170\) −6.45488 + 5.10769i −0.495067 + 0.391742i
\(171\) −7.96597 7.96597i −0.609173 0.609173i
\(172\) −8.45874 13.6913i −0.644973 1.04395i
\(173\) 5.63858 5.63858i 0.428694 0.428694i −0.459490 0.888183i \(-0.651968\pi\)
0.888183 + 0.459490i \(0.151968\pi\)
\(174\) 23.6747 + 2.75840i 1.79477 + 0.209114i
\(175\) −9.88030 −0.746880
\(176\) 1.64353 + 4.93569i 0.123886 + 0.372041i
\(177\) −4.67893 −0.351690
\(178\) 11.8824 + 1.38445i 0.890626 + 0.103769i
\(179\) 11.7278 11.7278i 0.876575 0.876575i −0.116604 0.993179i \(-0.537201\pi\)
0.993179 + 0.116604i \(0.0372007\pi\)
\(180\) −35.7444 + 22.0836i −2.66423 + 1.64601i
\(181\) −4.18574 4.18574i −0.311124 0.311124i 0.534221 0.845345i \(-0.320605\pi\)
−0.845345 + 0.534221i \(0.820605\pi\)
\(182\) −1.76611 + 1.39751i −0.130913 + 0.103590i
\(183\) 13.2293i 0.977937i
\(184\) 12.6838 + 4.60078i 0.935064 + 0.339174i
\(185\) 9.02674i 0.663659i
\(186\) 10.4819 + 13.2465i 0.768569 + 0.971284i
\(187\) −1.38756 1.38756i −0.101469 0.101469i
\(188\) −7.00223 1.65415i −0.510690 0.120641i
\(189\) −5.02656 + 5.02656i −0.365629 + 0.365629i
\(190\) 1.30599 11.2090i 0.0947464 0.813187i
\(191\) 12.3676 0.894891 0.447445 0.894311i \(-0.352334\pi\)
0.447445 + 0.894311i \(0.352334\pi\)
\(192\) 23.1567 2.07717i 1.67119 0.149907i
\(193\) 23.6837 1.70479 0.852395 0.522898i \(-0.175149\pi\)
0.852395 + 0.522898i \(0.175149\pi\)
\(194\) 2.65512 22.7883i 0.190626 1.63610i
\(195\) 12.6240 12.6240i 0.904026 0.904026i
\(196\) 1.94643 + 0.459808i 0.139030 + 0.0328434i
\(197\) −11.4195 11.4195i −0.813606 0.813606i 0.171566 0.985173i \(-0.445117\pi\)
−0.985173 + 0.171566i \(0.945117\pi\)
\(198\) −6.21546 7.85482i −0.441713 0.558218i
\(199\) 5.49683i 0.389660i 0.980837 + 0.194830i \(0.0624155\pi\)
−0.980837 + 0.194830i \(0.937585\pi\)
\(200\) −26.2708 9.52917i −1.85763 0.673814i
\(201\) 6.27351i 0.442499i
\(202\) −18.1406 + 14.3545i −1.27636 + 1.00998i
\(203\) 4.10069 + 4.10069i 0.287812 + 0.287812i
\(204\) −7.46098 + 4.60954i −0.522373 + 0.322732i
\(205\) 20.3356 20.3356i 1.42030 1.42030i
\(206\) −24.1435 2.81302i −1.68216 0.195992i
\(207\) −25.9792 −1.80568
\(208\) −6.04377 + 2.01251i −0.419060 + 0.139542i
\(209\) 2.69027 0.186090
\(210\) −15.7478 1.83481i −1.08670 0.126614i
\(211\) 0.907874 0.907874i 0.0625007 0.0625007i −0.675166 0.737666i \(-0.735928\pi\)
0.737666 + 0.675166i \(0.235928\pi\)
\(212\) 1.00453 + 1.62593i 0.0689914 + 0.111669i
\(213\) 28.4005 + 28.4005i 1.94597 + 1.94597i
\(214\) 6.43260 5.09006i 0.439723 0.347949i
\(215\) 31.0404i 2.11694i
\(216\) −18.2131 + 8.51726i −1.23925 + 0.579526i
\(217\) 4.10999i 0.279004i
\(218\) 4.06257 + 5.13410i 0.275152 + 0.347725i
\(219\) −29.7458 29.7458i −2.01004 2.01004i
\(220\) 2.30677 9.76484i 0.155522 0.658345i
\(221\) 1.69908 1.69908i 0.114292 0.114292i
\(222\) 1.11304 9.55297i 0.0747023 0.641153i
\(223\) −3.20318 −0.214501 −0.107250 0.994232i \(-0.534205\pi\)
−0.107250 + 0.994232i \(0.534205\pi\)
\(224\) 4.73191 + 3.09984i 0.316164 + 0.207117i
\(225\) 53.8083 3.58722
\(226\) −1.50114 + 12.8839i −0.0998540 + 0.857025i
\(227\) −13.7931 + 13.7931i −0.915480 + 0.915480i −0.996696 0.0812167i \(-0.974119\pi\)
0.0812167 + 0.996696i \(0.474119\pi\)
\(228\) 2.76425 11.7014i 0.183067 0.774945i
\(229\) 7.02177 + 7.02177i 0.464012 + 0.464012i 0.899968 0.435956i \(-0.143590\pi\)
−0.435956 + 0.899968i \(0.643590\pi\)
\(230\) −16.1482 20.4074i −1.06478 1.34562i
\(231\) 3.77961i 0.248680i
\(232\) 6.94841 + 14.8583i 0.456185 + 0.975496i
\(233\) 2.93857i 0.192512i 0.995357 + 0.0962561i \(0.0306868\pi\)
−0.995357 + 0.0962561i \(0.969313\pi\)
\(234\) 9.61826 7.61085i 0.628765 0.497537i
\(235\) 9.81272 + 9.81272i 0.640111 + 0.640111i
\(236\) −1.69241 2.73932i −0.110166 0.178315i
\(237\) 3.65710 3.65710i 0.237554 0.237554i
\(238\) −2.11950 0.246948i −0.137387 0.0160073i
\(239\) 16.2109 1.04859 0.524297 0.851536i \(-0.324328\pi\)
0.524297 + 0.851536i \(0.324328\pi\)
\(240\) −40.1023 20.0667i −2.58859 1.29530i
\(241\) −14.1166 −0.909329 −0.454665 0.890663i \(-0.650241\pi\)
−0.454665 + 0.890663i \(0.650241\pi\)
\(242\) −13.0759 1.52351i −0.840552 0.0979347i
\(243\) −6.19990 + 6.19990i −0.397724 + 0.397724i
\(244\) 7.74522 4.78515i 0.495837 0.306338i
\(245\) −2.72766 2.72766i −0.174264 0.174264i
\(246\) 24.0286 19.0136i 1.53201 1.21227i
\(247\) 3.29424i 0.209608i
\(248\) −3.96393 + 10.9281i −0.251710 + 0.693936i
\(249\) 29.4330i 1.86524i
\(250\) 16.5206 + 20.8779i 1.04485 + 1.32044i
\(251\) −14.1967 14.1967i −0.896091 0.896091i 0.0989969 0.995088i \(-0.468437\pi\)
−0.995088 + 0.0989969i \(0.968437\pi\)
\(252\) −10.6003 2.50412i −0.667755 0.157745i
\(253\) 4.38685 4.38685i 0.275799 0.275799i
\(254\) −2.12417 + 18.2313i −0.133282 + 1.14393i
\(255\) 16.9153 1.05927
\(256\) 9.59206 + 12.8060i 0.599503 + 0.800372i
\(257\) −3.23679 −0.201905 −0.100953 0.994891i \(-0.532189\pi\)
−0.100953 + 0.994891i \(0.532189\pi\)
\(258\) −3.82742 + 32.8499i −0.238285 + 2.04515i
\(259\) 1.65467 1.65467i 0.102816 0.102816i
\(260\) 11.9571 + 2.82464i 0.741547 + 0.175177i
\(261\) −22.3324 22.3324i −1.38234 1.38234i
\(262\) 8.46350 + 10.6958i 0.522877 + 0.660788i
\(263\) 24.0161i 1.48090i 0.672114 + 0.740448i \(0.265386\pi\)
−0.672114 + 0.740448i \(0.734614\pi\)
\(264\) 3.64529 10.0497i 0.224352 0.618514i
\(265\) 3.68624i 0.226444i
\(266\) 2.29409 1.81529i 0.140659 0.111303i
\(267\) −17.3832 17.3832i −1.06383 1.06383i
\(268\) 3.67289 2.26918i 0.224357 0.138612i
\(269\) −0.0875040 + 0.0875040i −0.00533521 + 0.00533521i −0.709769 0.704434i \(-0.751201\pi\)
0.704434 + 0.709769i \(0.251201\pi\)
\(270\) 38.5193 + 4.48798i 2.34421 + 0.273130i
\(271\) −10.1138 −0.614372 −0.307186 0.951650i \(-0.599387\pi\)
−0.307186 + 0.951650i \(0.599387\pi\)
\(272\) −5.39739 2.70079i −0.327265 0.163760i
\(273\) 4.62815 0.280109
\(274\) −31.8227 3.70774i −1.92248 0.223993i
\(275\) −9.08608 + 9.08608i −0.547911 + 0.547911i
\(276\) −14.5733 23.5882i −0.877208 1.41984i
\(277\) −11.0080 11.0080i −0.661406 0.661406i 0.294305 0.955711i \(-0.404912\pi\)
−0.955711 + 0.294305i \(0.904912\pi\)
\(278\) −10.4254 + 8.24957i −0.625277 + 0.494776i
\(279\) 22.3831i 1.34004i
\(280\) −4.62189 9.88334i −0.276211 0.590643i
\(281\) 4.21999i 0.251743i −0.992047 0.125872i \(-0.959827\pi\)
0.992047 0.125872i \(-0.0401727\pi\)
\(282\) 9.17481 + 11.5947i 0.546352 + 0.690455i
\(283\) −16.5834 16.5834i −0.985781 0.985781i 0.0141195 0.999900i \(-0.495505\pi\)
−0.999900 + 0.0141195i \(0.995505\pi\)
\(284\) −6.35464 + 26.9000i −0.377079 + 1.59622i
\(285\) −16.3980 + 16.3980i −0.971334 + 0.971334i
\(286\) −0.338971 + 2.90931i −0.0200438 + 0.172031i
\(287\) 7.45533 0.440074
\(288\) −25.7701 16.8818i −1.51852 0.994770i
\(289\) −14.7234 −0.866080
\(290\) 3.66131 31.4242i 0.215000 1.84529i
\(291\) −33.3377 + 33.3377i −1.95429 + 1.95429i
\(292\) 6.65566 28.1743i 0.389493 1.64878i
\(293\) −13.5242 13.5242i −0.790093 0.790093i 0.191416 0.981509i \(-0.438692\pi\)
−0.981509 + 0.191416i \(0.938692\pi\)
\(294\) −2.55034 3.22301i −0.148739 0.187970i
\(295\) 6.21049i 0.361589i
\(296\) 5.99547 2.80375i 0.348480 0.162965i
\(297\) 9.24501i 0.536450i
\(298\) 12.1868 9.64330i 0.705961 0.558621i
\(299\) 5.37171 + 5.37171i 0.310654 + 0.310654i
\(300\) 30.1843 + 48.8561i 1.74269 + 2.82071i
\(301\) −5.68992 + 5.68992i −0.327962 + 0.327962i
\(302\) 7.68137 + 0.894976i 0.442013 + 0.0515001i
\(303\) 47.5380 2.73099
\(304\) 7.85056 2.61415i 0.450260 0.149932i
\(305\) −17.5597 −1.00546
\(306\) 11.5428 + 1.34488i 0.659860 + 0.0768820i
\(307\) −8.93389 + 8.93389i −0.509884 + 0.509884i −0.914491 0.404607i \(-0.867408\pi\)
0.404607 + 0.914491i \(0.367408\pi\)
\(308\) 2.21281 1.36712i 0.126087 0.0778988i
\(309\) 35.3203 + 35.3203i 2.00930 + 2.00930i
\(310\) 17.5826 13.9130i 0.998623 0.790203i
\(311\) 19.7737i 1.12126i 0.828066 + 0.560631i \(0.189442\pi\)
−0.828066 + 0.560631i \(0.810558\pi\)
\(312\) 12.3058 + 4.46368i 0.696682 + 0.252706i
\(313\) 8.72743i 0.493303i 0.969104 + 0.246652i \(0.0793304\pi\)
−0.969104 + 0.246652i \(0.920670\pi\)
\(314\) 6.97122 + 8.80992i 0.393409 + 0.497173i
\(315\) 14.8549 + 14.8549i 0.836979 + 0.836979i
\(316\) 3.46389 + 0.818280i 0.194859 + 0.0460319i
\(317\) 19.0197 19.0197i 1.06825 1.06825i 0.0707615 0.997493i \(-0.477457\pi\)
0.997493 0.0707615i \(-0.0225429\pi\)
\(318\) 0.454531 3.90114i 0.0254888 0.218765i
\(319\) 7.54211 0.422277
\(320\) −2.75710 30.7366i −0.154126 1.71823i
\(321\) −16.8569 −0.940858
\(322\) 0.780738 6.70090i 0.0435088 0.373427i
\(323\) −2.20702 + 2.20702i −0.122802 + 0.122802i
\(324\) 8.41065 + 1.98686i 0.467258 + 0.110381i
\(325\) −11.1259 11.1259i −0.617156 0.617156i
\(326\) 7.84039 + 9.90834i 0.434239 + 0.548772i
\(327\) 13.4541i 0.744013i
\(328\) 19.8231 + 7.19038i 1.09455 + 0.397022i
\(329\) 3.59748i 0.198336i
\(330\) −16.1692 + 12.7946i −0.890086 + 0.704318i
\(331\) 22.3328 + 22.3328i 1.22752 + 1.22752i 0.964899 + 0.262620i \(0.0845866\pi\)
0.262620 + 0.964899i \(0.415413\pi\)
\(332\) 17.2318 10.6462i 0.945720 0.584284i
\(333\) −9.01134 + 9.01134i −0.493818 + 0.493818i
\(334\) −16.6001 1.93412i −0.908318 0.105830i
\(335\) −8.32703 −0.454954
\(336\) −3.67267 11.0294i −0.200360 0.601704i
\(337\) −23.4825 −1.27918 −0.639588 0.768718i \(-0.720895\pi\)
−0.639588 + 0.768718i \(0.720895\pi\)
\(338\) 14.6988 + 1.71259i 0.799508 + 0.0931527i
\(339\) 18.8483 18.8483i 1.02370 1.02370i
\(340\) 6.11839 + 9.90320i 0.331816 + 0.537076i
\(341\) 3.77961 + 3.77961i 0.204678 + 0.204678i
\(342\) −12.4936 + 9.88612i −0.675579 + 0.534580i
\(343\) 1.00000i 0.0539949i
\(344\) −20.6167 + 9.64129i −1.11158 + 0.519824i
\(345\) 53.4784i 2.87918i
\(346\) −6.99774 8.84343i −0.376201 0.475426i
\(347\) −6.29716 6.29716i −0.338049 0.338049i 0.517584 0.855633i \(-0.326832\pi\)
−0.855633 + 0.517584i \(0.826832\pi\)
\(348\) 7.74950 32.8047i 0.415417 1.75851i
\(349\) 6.94033 6.94033i 0.371507 0.371507i −0.496519 0.868026i \(-0.665389\pi\)
0.868026 + 0.496519i \(0.165389\pi\)
\(350\) −1.61707 + 13.8790i −0.0864361 + 0.741862i
\(351\) −11.3206 −0.604246
\(352\) 7.20220 1.50088i 0.383879 0.0799969i
\(353\) 30.0934 1.60171 0.800856 0.598857i \(-0.204378\pi\)
0.800856 + 0.598857i \(0.204378\pi\)
\(354\) −0.765783 + 6.57254i −0.0407009 + 0.349327i
\(355\) 37.6969 37.6969i 2.00074 2.00074i
\(356\) 3.88951 16.4648i 0.206144 0.872633i
\(357\) 3.10069 + 3.10069i 0.164106 + 0.164106i
\(358\) −14.5547 18.3936i −0.769239 0.972131i
\(359\) 10.3716i 0.547394i 0.961816 + 0.273697i \(0.0882465\pi\)
−0.961816 + 0.273697i \(0.911754\pi\)
\(360\) 25.1709 + 53.8249i 1.32662 + 2.83682i
\(361\) 14.7209i 0.774786i
\(362\) −6.56482 + 5.19469i −0.345039 + 0.273027i
\(363\) 19.1292 + 19.1292i 1.00402 + 1.00402i
\(364\) 1.67404 + 2.70960i 0.0877436 + 0.142021i
\(365\) −39.4826 + 39.4826i −2.06661 + 2.06661i
\(366\) −18.5833 2.16519i −0.971366 0.113176i
\(367\) −8.12973 −0.424368 −0.212184 0.977230i \(-0.568058\pi\)
−0.212184 + 0.977230i \(0.568058\pi\)
\(368\) 8.53868 17.0641i 0.445109 0.889529i
\(369\) −40.6019 −2.11365
\(370\) −12.6800 1.47737i −0.659200 0.0768050i
\(371\) 0.675714 0.675714i 0.0350813 0.0350813i
\(372\) 20.3231 12.5560i 1.05370 0.650999i
\(373\) −3.18688 3.18688i −0.165010 0.165010i 0.619772 0.784782i \(-0.287225\pi\)
−0.784782 + 0.619772i \(0.787225\pi\)
\(374\) −2.17622 + 1.72203i −0.112530 + 0.0890440i
\(375\) 54.7115i 2.82529i
\(376\) −3.46963 + 9.56539i −0.178933 + 0.493297i
\(377\) 9.23534i 0.475644i
\(378\) 6.23819 + 7.88355i 0.320858 + 0.405486i
\(379\) −0.839080 0.839080i −0.0431006 0.0431006i 0.685228 0.728329i \(-0.259703\pi\)
−0.728329 + 0.685228i \(0.759703\pi\)
\(380\) −15.5317 3.66907i −0.796758 0.188219i
\(381\) 26.6711 26.6711i 1.36640 1.36640i
\(382\) 2.02417 17.3730i 0.103565 0.888878i
\(383\) −34.3749 −1.75647 −0.878237 0.478225i \(-0.841280\pi\)
−0.878237 + 0.478225i \(0.841280\pi\)
\(384\) 0.872140 32.8684i 0.0445062 1.67731i
\(385\) −5.01680 −0.255680
\(386\) 3.87623 33.2688i 0.197295 1.69334i
\(387\) 30.9874 30.9874i 1.57518 1.57518i
\(388\) −31.5764 7.45934i −1.60305 0.378691i
\(389\) 10.9633 + 10.9633i 0.555860 + 0.555860i 0.928126 0.372266i \(-0.121419\pi\)
−0.372266 + 0.928126i \(0.621419\pi\)
\(390\) −15.6670 19.7993i −0.793329 1.00257i
\(391\) 7.19768i 0.364003i
\(392\) 0.964462 2.65891i 0.0487127 0.134295i
\(393\) 28.0287i 1.41386i
\(394\) −17.9101 + 14.1721i −0.902298 + 0.713981i
\(395\) −4.85419 4.85419i −0.244241 0.244241i
\(396\) −12.0510 + 7.44535i −0.605586 + 0.374143i
\(397\) 26.4375 26.4375i 1.32686 1.32686i 0.418764 0.908095i \(-0.362463\pi\)
0.908095 0.418764i \(-0.137537\pi\)
\(398\) 7.72146 + 0.899646i 0.387042 + 0.0450952i
\(399\) −6.01174 −0.300963
\(400\) −17.6854 + 35.3433i −0.884269 + 1.76717i
\(401\) 4.97625 0.248502 0.124251 0.992251i \(-0.460347\pi\)
0.124251 + 0.992251i \(0.460347\pi\)
\(402\) −8.81247 1.02676i −0.439526 0.0512102i
\(403\) −4.62815 + 4.62815i −0.230545 + 0.230545i
\(404\) 17.1949 + 27.8316i 0.855478 + 1.38467i
\(405\) −11.7864 11.7864i −0.585672 0.585672i
\(406\) 6.43142 5.08913i 0.319186 0.252569i
\(407\) 3.04331i 0.150851i
\(408\) 5.25396 + 11.2349i 0.260110 + 0.556212i
\(409\) 4.06359i 0.200932i 0.994941 + 0.100466i \(0.0320333\pi\)
−0.994941 + 0.100466i \(0.967967\pi\)
\(410\) −25.2374 31.8939i −1.24639 1.57513i
\(411\) 46.5544 + 46.5544i 2.29636 + 2.29636i
\(412\) −7.90295 + 33.4542i −0.389350 + 1.64817i
\(413\) −1.13843 + 1.13843i −0.0560184 + 0.0560184i
\(414\) −4.25192 + 36.4932i −0.208970 + 1.79354i
\(415\) −39.0674 −1.91774
\(416\) 1.83783 + 8.81913i 0.0901069 + 0.432393i
\(417\) 27.3203 1.33788
\(418\) 0.440306 3.77905i 0.0215361 0.184839i
\(419\) 0.552238 0.552238i 0.0269786 0.0269786i −0.693489 0.720467i \(-0.743927\pi\)
0.720467 + 0.693489i \(0.243927\pi\)
\(420\) −5.15476 + 21.8208i −0.251526 + 1.06474i
\(421\) −3.77763 3.77763i −0.184110 0.184110i 0.609034 0.793144i \(-0.291557\pi\)
−0.793144 + 0.609034i \(0.791557\pi\)
\(422\) −1.12671 1.42389i −0.0548475 0.0693139i
\(423\) 19.5920i 0.952593i
\(424\) 2.44836 1.14496i 0.118903 0.0556044i
\(425\) 14.9079i 0.723140i
\(426\) 44.5427 35.2463i 2.15810 1.70769i
\(427\) −3.21881 3.21881i −0.155769 0.155769i
\(428\) −6.09727 9.86901i −0.294723 0.477037i
\(429\) 4.25612 4.25612i 0.205487 0.205487i
\(430\) 43.6028 + 5.08027i 2.10271 + 0.244992i
\(431\) 1.18186 0.0569283 0.0284641 0.999595i \(-0.490938\pi\)
0.0284641 + 0.999595i \(0.490938\pi\)
\(432\) 8.98342 + 26.9781i 0.432215 + 1.29799i
\(433\) −15.2584 −0.733273 −0.366637 0.930364i \(-0.619491\pi\)
−0.366637 + 0.930364i \(0.619491\pi\)
\(434\) 5.77335 + 0.672667i 0.277130 + 0.0322891i
\(435\) −45.9715 + 45.9715i −2.20416 + 2.20416i
\(436\) 7.87683 4.86646i 0.377232 0.233061i
\(437\) −6.97759 6.97759i −0.333783 0.333783i
\(438\) −46.6527 + 36.9159i −2.22915 + 1.76391i
\(439\) 4.34502i 0.207376i 0.994610 + 0.103688i \(0.0330644\pi\)
−0.994610 + 0.103688i \(0.966936\pi\)
\(440\) −13.3392 4.83851i −0.635923 0.230667i
\(441\) 5.44602i 0.259334i
\(442\) −2.10863 2.66479i −0.100297 0.126751i
\(443\) −4.31392 4.31392i −0.204961 0.204961i 0.597161 0.802121i \(-0.296295\pi\)
−0.802121 + 0.597161i \(0.796295\pi\)
\(444\) −13.2370 3.12700i −0.628200 0.148401i
\(445\) −23.0733 + 23.0733i −1.09378 + 1.09378i
\(446\) −0.524253 + 4.49954i −0.0248241 + 0.213060i
\(447\) −31.9359 −1.51052
\(448\) 5.12884 6.13963i 0.242315 0.290070i
\(449\) 3.72499 0.175793 0.0878967 0.996130i \(-0.471985\pi\)
0.0878967 + 0.996130i \(0.471985\pi\)
\(450\) 8.80661 75.5851i 0.415147 3.56312i
\(451\) 6.85604 6.85604i 0.322838 0.322838i
\(452\) 17.8525 + 4.21732i 0.839710 + 0.198366i
\(453\) −11.2373 11.2373i −0.527976 0.527976i
\(454\) 17.1178 + 21.6328i 0.803380 + 1.01528i
\(455\) 6.14310i 0.287993i
\(456\) −15.9847 5.79809i −0.748552 0.271521i
\(457\) 10.7451i 0.502636i 0.967905 + 0.251318i \(0.0808640\pi\)
−0.967905 + 0.251318i \(0.919136\pi\)
\(458\) 11.0128 8.71433i 0.514594 0.407194i
\(459\) −7.58434 7.58434i −0.354007 0.354007i
\(460\) −31.3094 + 19.3436i −1.45981 + 0.901899i
\(461\) 7.88785 7.88785i 0.367374 0.367374i −0.499145 0.866519i \(-0.666352\pi\)
0.866519 + 0.499145i \(0.166352\pi\)
\(462\) −5.30926 0.618595i −0.247009 0.0287797i
\(463\) 27.3485 1.27099 0.635496 0.772104i \(-0.280796\pi\)
0.635496 + 0.772104i \(0.280796\pi\)
\(464\) 22.0089 7.32870i 1.02174 0.340226i
\(465\) −46.0758 −2.13671
\(466\) 4.12784 + 0.480945i 0.191219 + 0.0222794i
\(467\) 11.3915 11.3915i 0.527135 0.527135i −0.392582 0.919717i \(-0.628418\pi\)
0.919717 + 0.392582i \(0.128418\pi\)
\(468\) −9.11686 14.7565i −0.421427 0.682120i
\(469\) −1.52640 1.52640i −0.0704828 0.0704828i
\(470\) 15.3900 12.1780i 0.709890 0.561730i
\(471\) 23.0867i 1.06378i
\(472\) −4.12495 + 1.92901i −0.189866 + 0.0887898i
\(473\) 10.4651i 0.481185i
\(474\) −4.53862 5.73571i −0.208466 0.263450i
\(475\) 14.4520 + 14.4520i 0.663105 + 0.663105i
\(476\) −0.693782 + 2.93687i −0.0317994 + 0.134611i
\(477\) −3.67995 + 3.67995i −0.168493 + 0.168493i
\(478\) 2.65317 22.7716i 0.121353 1.04155i
\(479\) 11.3880 0.520330 0.260165 0.965564i \(-0.416223\pi\)
0.260165 + 0.965564i \(0.416223\pi\)
\(480\) −34.7513 + 53.0479i −1.58617 + 2.42130i
\(481\) 3.72655 0.169916
\(482\) −2.31041 + 19.8297i −0.105236 + 0.903219i
\(483\) −9.80296 + 9.80296i −0.446050 + 0.446050i
\(484\) −4.28017 + 18.1185i −0.194553 + 0.823570i
\(485\) 44.2502 + 44.2502i 2.00930 + 2.00930i
\(486\) 7.69435 + 9.72378i 0.349023 + 0.441080i
\(487\) 31.3531i 1.42075i −0.703826 0.710373i \(-0.748526\pi\)
0.703826 0.710373i \(-0.251474\pi\)
\(488\) −5.45412 11.6630i −0.246896 0.527957i
\(489\) 25.9652i 1.17419i
\(490\) −4.27801 + 3.38515i −0.193261 + 0.152926i
\(491\) 20.2775 + 20.2775i 0.915112 + 0.915112i 0.996669 0.0815572i \(-0.0259893\pi\)
−0.0815572 + 0.996669i \(0.525989\pi\)
\(492\) −22.7760 36.8651i −1.02682 1.66201i
\(493\) −6.18733 + 6.18733i −0.278663 + 0.278663i
\(494\) 4.62746 + 0.539157i 0.208199 + 0.0242578i
\(495\) 27.3216 1.22802
\(496\) 14.7021 + 7.35674i 0.660143 + 0.330327i
\(497\) 13.8202 0.619921
\(498\) −41.3449 4.81719i −1.85271 0.215864i
\(499\) −18.5167 + 18.5167i −0.828921 + 0.828921i −0.987368 0.158446i \(-0.949351\pi\)
0.158446 + 0.987368i \(0.449351\pi\)
\(500\) 32.0313 19.7896i 1.43249 0.885017i
\(501\) 24.2848 + 24.2848i 1.08497 + 1.08497i
\(502\) −22.2659 + 17.6188i −0.993774 + 0.786366i
\(503\) 31.9854i 1.42616i −0.701082 0.713080i \(-0.747299\pi\)
0.701082 0.713080i \(-0.252701\pi\)
\(504\) −5.25248 + 14.4805i −0.233964 + 0.645012i
\(505\) 63.0987i 2.80786i
\(506\) −5.44427 6.88023i −0.242028 0.305864i
\(507\) −21.5033 21.5033i −0.954996 0.954996i
\(508\) 25.2620 + 5.96769i 1.12082 + 0.264774i
\(509\) 12.1644 12.1644i 0.539176 0.539176i −0.384111 0.923287i \(-0.625492\pi\)
0.923287 + 0.384111i \(0.125492\pi\)
\(510\) 2.76846 23.7610i 0.122589 1.05216i
\(511\) −14.4749 −0.640331
\(512\) 19.5586 11.3782i 0.864375 0.502849i
\(513\) 14.7048 0.649234
\(514\) −0.529753 + 4.54675i −0.0233664 + 0.200549i
\(515\) 46.8817 46.8817i 2.06586 2.06586i
\(516\) 45.5182 + 10.7529i 2.00383 + 0.473368i
\(517\) 3.30830 + 3.30830i 0.145499 + 0.145499i
\(518\) −2.05351 2.59514i −0.0902262 0.114024i
\(519\) 23.1745i 1.01725i
\(520\) 5.92478 16.3340i 0.259819 0.716291i
\(521\) 34.4322i 1.50850i −0.656586 0.754251i \(-0.728000\pi\)
0.656586 0.754251i \(-0.272000\pi\)
\(522\) −35.0257 + 27.7155i −1.53303 + 1.21308i
\(523\) −15.4031 15.4031i −0.673530 0.673530i 0.284998 0.958528i \(-0.408007\pi\)
−0.958528 + 0.284998i \(0.908007\pi\)
\(524\) 16.4097 10.1382i 0.716861 0.442890i
\(525\) 20.3040 20.3040i 0.886138 0.886138i
\(526\) 33.7357 + 3.93062i 1.47094 + 0.171383i
\(527\) −6.20137 −0.270136
\(528\) −13.5203 6.76537i −0.588394 0.294425i
\(529\) 0.244184 0.0106167
\(530\) −5.17810 0.603314i −0.224922 0.0262063i
\(531\) 6.19990 6.19990i 0.269053 0.269053i
\(532\) −2.17450 3.51963i −0.0942764 0.152595i
\(533\) 8.39524 + 8.39524i 0.363638 + 0.363638i
\(534\) −27.2634 + 21.5733i −1.17980 + 0.933569i
\(535\) 22.3747i 0.967341i
\(536\) −2.58642 5.53073i −0.111716 0.238891i
\(537\) 48.2011i 2.08003i
\(538\) 0.108596 + 0.137239i 0.00468192 + 0.00591681i
\(539\) −0.919616 0.919616i −0.0396106 0.0396106i
\(540\) 12.6086 53.3740i 0.542589 2.29685i
\(541\) −23.7164 + 23.7164i −1.01965 + 1.01965i −0.0198437 + 0.999803i \(0.506317\pi\)
−0.999803 + 0.0198437i \(0.993683\pi\)
\(542\) −1.65529 + 14.2070i −0.0711010 + 0.610244i
\(543\) 17.2034 0.738267
\(544\) −4.67720 + 7.13975i −0.200533 + 0.306114i
\(545\) −17.8581 −0.764956
\(546\) 0.757473 6.50122i 0.0324168 0.278226i
\(547\) 27.8819 27.8819i 1.19214 1.19214i 0.215680 0.976464i \(-0.430803\pi\)
0.976464 0.215680i \(-0.0691967\pi\)
\(548\) −10.4166 + 44.0949i −0.444975 + 1.88364i
\(549\) 17.5297 + 17.5297i 0.748150 + 0.748150i
\(550\) 11.2762 + 14.2504i 0.480820 + 0.607639i
\(551\) 11.9963i 0.511058i
\(552\) −35.5198 + 16.6106i −1.51182 + 0.706995i
\(553\) 1.77961i 0.0756769i
\(554\) −17.2647 + 13.6614i −0.733506 + 0.580418i
\(555\) 18.5499 + 18.5499i 0.787400 + 0.787400i
\(556\) 9.88197 + 15.9949i 0.419089 + 0.678335i
\(557\) 0.275943 0.275943i 0.0116921 0.0116921i −0.701237 0.712929i \(-0.747368\pi\)
0.712929 + 0.701237i \(0.247368\pi\)
\(558\) −31.4418 3.66336i −1.33104 0.155082i
\(559\) −12.8145 −0.541997
\(560\) −14.6397 + 4.87485i −0.618640 + 0.206000i
\(561\) 5.70288 0.240776
\(562\) −5.92786 0.690669i −0.250052 0.0291341i
\(563\) −13.8911 + 13.8911i −0.585438 + 0.585438i −0.936393 0.350954i \(-0.885857\pi\)
0.350954 + 0.936393i \(0.385857\pi\)
\(564\) 17.7888 10.9903i 0.749045 0.462775i
\(565\) −25.0179 25.0179i −1.05251 1.05251i
\(566\) −26.0090 + 20.5807i −1.09324 + 0.865073i
\(567\) 4.32107i 0.181468i
\(568\) 36.7467 + 13.3291i 1.54186 + 0.559275i
\(569\) 8.08076i 0.338763i −0.985551 0.169381i \(-0.945823\pi\)
0.985551 0.169381i \(-0.0541770\pi\)
\(570\) 20.3507 + 25.7183i 0.852395 + 1.07722i
\(571\) −7.55816 7.55816i −0.316299 0.316299i 0.531045 0.847344i \(-0.321800\pi\)
−0.847344 + 0.531045i \(0.821800\pi\)
\(572\) 4.03126 + 0.952312i 0.168556 + 0.0398182i
\(573\) −25.4154 + 25.4154i −1.06175 + 1.06175i
\(574\) 1.22019 10.4726i 0.0509296 0.437117i
\(575\) 47.1320 1.96554
\(576\) −27.9317 + 33.4365i −1.16382 + 1.39319i
\(577\) 1.95969 0.0815831 0.0407915 0.999168i \(-0.487012\pi\)
0.0407915 + 0.999168i \(0.487012\pi\)
\(578\) −2.40972 + 20.6821i −0.100231 + 0.860261i
\(579\) −48.6699 + 48.6699i −2.02265 + 2.02265i
\(580\) −43.5427 10.2862i −1.80801 0.427110i
\(581\) −7.16133 7.16133i −0.297102 0.297102i
\(582\) 41.3735 + 52.2860i 1.71499 + 2.16733i
\(583\) 1.24279i 0.0514713i
\(584\) −38.4874 13.9605i −1.59262 0.577688i
\(585\) 33.4554i 1.38321i
\(586\) −21.2111 + 16.7842i −0.876221 + 0.693347i
\(587\) 24.6131 + 24.6131i 1.01589 + 1.01589i 0.999872 + 0.0160192i \(0.00509930\pi\)
0.0160192 + 0.999872i \(0.494901\pi\)
\(588\) −4.94480 + 3.05500i −0.203920 + 0.125986i
\(589\) 6.01174 6.01174i 0.247709 0.247709i
\(590\) 8.72395 + 1.01645i 0.359159 + 0.0418465i
\(591\) 46.9341 1.93061
\(592\) −2.95720 8.88078i −0.121540 0.364998i
\(593\) 16.5483 0.679558 0.339779 0.940505i \(-0.389648\pi\)
0.339779 + 0.940505i \(0.389648\pi\)
\(594\) 12.9866 + 1.51310i 0.532845 + 0.0620831i
\(595\) 4.11564 4.11564i 0.168725 0.168725i
\(596\) −11.5515 18.6972i −0.473167 0.765866i
\(597\) −11.2960 11.2960i −0.462313 0.462313i
\(598\) 8.42487 6.66654i 0.344519 0.272615i
\(599\) 10.2649i 0.419412i 0.977764 + 0.209706i \(0.0672507\pi\)
−0.977764 + 0.209706i \(0.932749\pi\)
\(600\) 73.5689 34.4041i 3.00344 1.40454i
\(601\) 35.6586i 1.45455i 0.686348 + 0.727273i \(0.259213\pi\)
−0.686348 + 0.727273i \(0.740787\pi\)
\(602\) 7.06145 + 8.92394i 0.287803 + 0.363713i
\(603\) 8.31283 + 8.31283i 0.338524 + 0.338524i
\(604\) 2.51436 10.6436i 0.102308 0.433083i
\(605\) 25.3908 25.3908i 1.03228 1.03228i
\(606\) 7.78037 66.7772i 0.316056 2.71264i
\(607\) 23.1111 0.938052 0.469026 0.883184i \(-0.344605\pi\)
0.469026 + 0.883184i \(0.344605\pi\)
\(608\) −2.38725 11.4556i −0.0968157 0.464586i
\(609\) −16.8538 −0.682950
\(610\) −2.87393 + 24.6663i −0.116362 + 0.998708i
\(611\) −4.05103 + 4.05103i −0.163887 + 0.163887i
\(612\) 3.77835 15.9942i 0.152731 0.646529i
\(613\) −26.9200 26.9200i −1.08729 1.08729i −0.995807 0.0914813i \(-0.970840\pi\)
−0.0914813 0.995807i \(-0.529160\pi\)
\(614\) 11.0874 + 14.0117i 0.447449 + 0.565467i
\(615\) 83.5793i 3.37024i
\(616\) −1.55824 3.33211i −0.0627834 0.134255i
\(617\) 47.9337i 1.92974i 0.262732 + 0.964869i \(0.415377\pi\)
−0.262732 + 0.964869i \(0.584623\pi\)
\(618\) 55.3955 43.8340i 2.22833 1.76326i
\(619\) 4.05053 + 4.05053i 0.162805 + 0.162805i 0.783808 0.621003i \(-0.213275\pi\)
−0.621003 + 0.783808i \(0.713275\pi\)
\(620\) −16.6660 26.9755i −0.669323 1.08336i
\(621\) 23.9782 23.9782i 0.962213 0.962213i
\(622\) 27.7763 + 3.23629i 1.11373 + 0.129763i
\(623\) −8.45899 −0.338902
\(624\) 8.28423 16.5556i 0.331634 0.662755i
\(625\) −23.2188 −0.928752
\(626\) 12.2595 + 1.42839i 0.489989 + 0.0570898i
\(627\) −5.52849 + 5.52849i −0.220787 + 0.220787i
\(628\) 13.5164 8.35067i 0.539361 0.333228i
\(629\) 2.49664 + 2.49664i 0.0995477 + 0.0995477i
\(630\) 23.2981 18.4356i 0.928219 0.734492i
\(631\) 2.35784i 0.0938640i 0.998898 + 0.0469320i \(0.0149444\pi\)
−0.998898 + 0.0469320i \(0.985056\pi\)
\(632\) 1.71637 4.73184i 0.0682735 0.188222i
\(633\) 3.73136i 0.148308i
\(634\) −23.6043 29.8301i −0.937448 1.18471i
\(635\) −35.4014 35.4014i −1.40486 1.40486i
\(636\) −5.40558 1.27697i −0.214345 0.0506351i
\(637\) 1.12607 1.12607i 0.0446166 0.0446166i
\(638\) 1.23439 10.5945i 0.0488699 0.419440i
\(639\) −75.2652 −2.97744
\(640\) −43.6273 1.15762i −1.72452 0.0457590i
\(641\) −49.8415 −1.96862 −0.984311 0.176440i \(-0.943542\pi\)
−0.984311 + 0.176440i \(0.943542\pi\)
\(642\) −2.75890 + 23.6790i −0.108885 + 0.934536i
\(643\) −6.07975 + 6.07975i −0.239762 + 0.239762i −0.816751 0.576990i \(-0.804227\pi\)
0.576990 + 0.816751i \(0.304227\pi\)
\(644\) −9.28505 2.19342i −0.365882 0.0864330i
\(645\) −63.7879 63.7879i −2.51165 2.51165i
\(646\) 2.73901 + 3.46144i 0.107765 + 0.136188i
\(647\) 0.463264i 0.0182128i −0.999959 0.00910640i \(-0.997101\pi\)
0.999959 0.00910640i \(-0.00289870\pi\)
\(648\) 4.16751 11.4894i 0.163715 0.451344i
\(649\) 2.09383i 0.0821901i
\(650\) −17.4497 + 13.8078i −0.684432 + 0.541586i
\(651\) −8.44602 8.44602i −0.331026 0.331026i
\(652\) 15.2016 9.39183i 0.595339 0.367812i
\(653\) 6.63668 6.63668i 0.259713 0.259713i −0.565224 0.824937i \(-0.691210\pi\)
0.824937 + 0.565224i \(0.191210\pi\)
\(654\) −18.8991 2.20198i −0.739014 0.0861044i
\(655\) −37.2034 −1.45366
\(656\) 13.3448 26.6689i 0.521026 1.04124i
\(657\) 78.8305 3.07547
\(658\) 5.05342 + 0.588786i 0.197003 + 0.0229533i
\(659\) −4.62922 + 4.62922i −0.180329 + 0.180329i −0.791499 0.611170i \(-0.790699\pi\)
0.611170 + 0.791499i \(0.290699\pi\)
\(660\) 15.3263 + 24.8071i 0.596576 + 0.965615i
\(661\) −2.25711 2.25711i −0.0877916 0.0877916i 0.661847 0.749639i \(-0.269773\pi\)
−0.749639 + 0.661847i \(0.769773\pi\)
\(662\) 35.0262 27.7160i 1.36133 1.07721i
\(663\) 6.98320i 0.271205i
\(664\) −12.1345 25.9482i −0.470911 1.00698i
\(665\) 7.97958i 0.309435i
\(666\) 11.1835 + 14.1332i 0.433351 + 0.547650i
\(667\) −19.5615 19.5615i −0.757425 0.757425i
\(668\) −5.43376 + 23.0018i −0.210239 + 0.889968i
\(669\) 6.58253 6.58253i 0.254495 0.254495i
\(670\) −1.36286 + 11.6971i −0.0526517 + 0.451898i
\(671\) −5.92014 −0.228544
\(672\) −16.0942 + 3.35389i −0.620848 + 0.129379i
\(673\) 6.82222 0.262977 0.131489 0.991318i \(-0.458024\pi\)
0.131489 + 0.991318i \(0.458024\pi\)
\(674\) −3.84330 + 32.9862i −0.148038 + 1.27058i
\(675\) −49.6639 + 49.6639i −1.91157 + 1.91157i
\(676\) 4.81139 20.3673i 0.185054 0.783356i
\(677\) 4.77844 + 4.77844i 0.183650 + 0.183650i 0.792944 0.609294i \(-0.208547\pi\)
−0.609294 + 0.792944i \(0.708547\pi\)
\(678\) −23.3916 29.5612i −0.898347 1.13529i
\(679\) 16.2227i 0.622571i
\(680\) 14.9125 6.97375i 0.571868 0.267431i
\(681\) 56.6895i 2.17235i
\(682\) 5.92786 4.69067i 0.226990 0.179615i
\(683\) −29.2736 29.2736i −1.12012 1.12012i −0.991723 0.128400i \(-0.959016\pi\)
−0.128400 0.991723i \(-0.540984\pi\)
\(684\) 11.8424 + 19.1680i 0.452804 + 0.732906i
\(685\) 61.7932 61.7932i 2.36100 2.36100i
\(686\) −1.40471 0.163666i −0.0536321 0.00624881i
\(687\) −28.8594 −1.10106
\(688\) 10.1690 + 30.5385i 0.387688 + 1.16427i
\(689\) 1.52181 0.0579762
\(690\) 75.1216 + 8.75261i 2.85983 + 0.333206i
\(691\) −4.65064 + 4.65064i −0.176919 + 0.176919i −0.790011 0.613092i \(-0.789925\pi\)
0.613092 + 0.790011i \(0.289925\pi\)
\(692\) −13.5678 + 8.38243i −0.515769 + 0.318652i
\(693\) 5.00824 + 5.00824i 0.190247 + 0.190247i
\(694\) −9.87632 + 7.81505i −0.374900 + 0.296655i
\(695\) 36.2631i 1.37554i
\(696\) −44.8127 16.2548i −1.69862 0.616138i
\(697\) 11.2490i 0.426086i
\(698\) −8.61326 10.8851i −0.326017 0.412005i
\(699\) −6.03875 6.03875i −0.228407 0.228407i
\(700\) 19.2313 + 4.54304i 0.726874 + 0.171711i
\(701\) −4.01206 + 4.01206i −0.151533 + 0.151533i −0.778802 0.627269i \(-0.784173\pi\)
0.627269 + 0.778802i \(0.284173\pi\)
\(702\) −1.85279 + 15.9021i −0.0699292 + 0.600186i
\(703\) −4.84060 −0.182567
\(704\) −0.929538 10.3627i −0.0350333 0.390557i
\(705\) −40.3302 −1.51892
\(706\) 4.92528 42.2726i 0.185365 1.59095i
\(707\) 11.5664 11.5664i 0.435001 0.435001i
\(708\) 9.10719 + 2.15141i 0.342269 + 0.0808549i
\(709\) 36.0117 + 36.0117i 1.35245 + 1.35245i 0.882915 + 0.469533i \(0.155578\pi\)
0.469533 + 0.882915i \(0.344422\pi\)
\(710\) −46.7835 59.1230i −1.75575 2.21885i
\(711\) 9.69181i 0.363471i
\(712\) −22.4917 8.15837i −0.842912 0.305748i
\(713\) 19.6059i 0.734248i
\(714\) 4.86304 3.84809i 0.181995 0.144011i
\(715\) −5.64929 5.64929i −0.211271 0.211271i
\(716\) −28.2198 + 17.4347i −1.05462 + 0.651566i
\(717\) −33.3133 + 33.3133i −1.24411 + 1.24411i
\(718\) 14.5691 + 1.69749i 0.543716 + 0.0633496i
\(719\) 7.62249 0.284271 0.142135 0.989847i \(-0.454603\pi\)
0.142135 + 0.989847i \(0.454603\pi\)
\(720\) 79.7281 26.5485i 2.97129 0.989406i
\(721\) 17.1875 0.640096
\(722\) 20.6787 + 2.40932i 0.769580 + 0.0896657i
\(723\) 29.0095 29.0095i 1.07888 1.07888i
\(724\) 6.22260 + 10.0719i 0.231261 + 0.374318i
\(725\) 40.5160 + 40.5160i 1.50473 + 1.50473i
\(726\) 30.0018 23.7402i 1.11347 0.881080i
\(727\) 25.4856i 0.945207i −0.881275 0.472604i \(-0.843314\pi\)
0.881275 0.472604i \(-0.156686\pi\)
\(728\) 4.08018 1.90808i 0.151222 0.0707180i
\(729\) 38.4448i 1.42388i
\(730\) 48.9997 + 61.9236i 1.81356 + 2.29190i
\(731\) −8.58525 8.58525i −0.317537 0.317537i
\(732\) −6.08293 + 25.7498i −0.224832 + 0.951742i
\(733\) −14.9748 + 14.9748i −0.553106 + 0.553106i −0.927336 0.374230i \(-0.877907\pi\)
0.374230 + 0.927336i \(0.377907\pi\)
\(734\) −1.33056 + 11.4199i −0.0491120 + 0.421517i
\(735\) 11.2107 0.413512
\(736\) −22.5727 14.7872i −0.832039 0.545063i
\(737\) −2.80741 −0.103412
\(738\) −6.64516 + 57.0339i −0.244612 + 2.09945i
\(739\) −12.3417 + 12.3417i −0.453996 + 0.453996i −0.896679 0.442682i \(-0.854027\pi\)
0.442682 + 0.896679i \(0.354027\pi\)
\(740\) −4.15057 + 17.5699i −0.152578 + 0.645882i
\(741\) −6.76966 6.76966i −0.248690 0.248690i
\(742\) −0.838591 1.05977i −0.0307857 0.0389056i
\(743\) 10.6724i 0.391531i 0.980651 + 0.195766i \(0.0627192\pi\)
−0.980651 + 0.195766i \(0.937281\pi\)
\(744\) −14.3114 30.6031i −0.524680 1.12196i
\(745\) 42.3896i 1.55303i
\(746\) −4.99823 + 3.95506i −0.182998 + 0.144805i
\(747\) 39.0007 + 39.0007i 1.42696 + 1.42696i
\(748\) 2.06278 + 3.33880i 0.0754226 + 0.122079i
\(749\) −4.10143 + 4.10143i −0.149863 + 0.149863i
\(750\) −76.8538 8.95442i −2.80630 0.326969i
\(751\) −2.82952 −0.103251 −0.0516254 0.998667i \(-0.516440\pi\)
−0.0516254 + 0.998667i \(0.516440\pi\)
\(752\) 12.8687 + 6.43936i 0.469275 + 0.234819i
\(753\) 58.3485 2.12634
\(754\) 12.9730 + 1.51151i 0.472448 + 0.0550461i
\(755\) −14.9157 + 14.9157i −0.542837 + 0.542837i
\(756\) 12.0951 7.47258i 0.439894 0.271775i
\(757\) 15.6590 + 15.6590i 0.569136 + 0.569136i 0.931886 0.362750i \(-0.118162\pi\)
−0.362750 + 0.931886i \(0.618162\pi\)
\(758\) −1.31599 + 1.04134i −0.0477990 + 0.0378230i
\(759\) 18.0299i 0.654444i
\(760\) −7.69600 + 21.2170i −0.279163 + 0.769622i
\(761\) 4.79367i 0.173770i 0.996218 + 0.0868852i \(0.0276913\pi\)
−0.996218 + 0.0868852i \(0.972309\pi\)
\(762\) −33.1001 41.8304i −1.19909 1.51535i
\(763\) −3.27351 3.27351i −0.118509 0.118509i
\(764\) −24.0727 5.68674i −0.870920 0.205739i
\(765\) −22.4139 + 22.4139i −0.810375 + 0.810375i
\(766\) −5.62601 + 48.2868i −0.203276 + 1.74467i
\(767\) −2.56390 −0.0925772
\(768\) −46.0278 6.60455i −1.66089 0.238321i
\(769\) 13.5489 0.488585 0.244293 0.969702i \(-0.421444\pi\)
0.244293 + 0.969702i \(0.421444\pi\)
\(770\) −0.821082 + 7.04716i −0.0295897 + 0.253962i
\(771\) 6.65159 6.65159i 0.239551 0.239551i
\(772\) −46.0986 10.8900i −1.65913 0.391938i
\(773\) 18.7803 + 18.7803i 0.675480 + 0.675480i 0.958974 0.283494i \(-0.0914936\pi\)
−0.283494 + 0.958974i \(0.591494\pi\)
\(774\) −38.4568 48.6000i −1.38230 1.74689i
\(775\) 40.6080i 1.45868i
\(776\) −15.6462 + 43.1348i −0.561666 + 1.54845i
\(777\) 6.80066i 0.243972i
\(778\) 17.1945 13.6059i 0.616454 0.487795i
\(779\) −10.9050 10.9050i −0.390712 0.390712i
\(780\) −30.3764 + 18.7671i −1.08765 + 0.671971i
\(781\) 12.7093 12.7093i 0.454774 0.454774i
\(782\) 10.1107 + 1.17802i 0.361557 + 0.0421259i
\(783\) 41.2247 1.47325
\(784\) −3.57715 1.78996i −0.127755 0.0639273i
\(785\) −30.6438 −1.09372
\(786\) −39.3723 4.58736i −1.40436 0.163626i
\(787\) 24.4838 24.4838i 0.872752 0.872752i −0.120020 0.992772i \(-0.538296\pi\)
0.992772 + 0.120020i \(0.0382958\pi\)
\(788\) 16.9765 + 27.4780i 0.604761 + 0.978864i
\(789\) −49.3530 49.3530i −1.75701 1.75701i
\(790\) −7.61320 + 6.02426i −0.270865 + 0.214334i
\(791\) 9.17193i 0.326116i
\(792\) 8.48622 + 18.1467i 0.301545 + 0.644816i
\(793\) 7.24923i 0.257428i
\(794\) −32.8101 41.4640i −1.16439 1.47150i
\(795\) 7.57521 + 7.57521i 0.268665 + 0.268665i
\(796\) 2.52748 10.6992i 0.0895843 0.379222i
\(797\) −17.6690 + 17.6690i −0.625870 + 0.625870i −0.947026 0.321157i \(-0.895928\pi\)
0.321157 + 0.947026i \(0.395928\pi\)
\(798\) −0.983920 + 8.44476i −0.0348304 + 0.298941i
\(799\) −5.42807 −0.192031
\(800\) 46.7527 + 30.6274i 1.65296 + 1.08284i
\(801\) 46.0678 1.62773
\(802\) 0.814444 6.99019i 0.0287590 0.246832i
\(803\) −13.3113 + 13.3113i −0.469746 + 0.469746i
\(804\) −2.88461 + 12.2109i −0.101732 + 0.430646i
\(805\) 13.0118 + 13.0118i 0.458605 + 0.458605i
\(806\) 5.74374 + 7.25869i 0.202315 + 0.255676i
\(807\) 0.359641i 0.0126600i
\(808\) 41.9096 19.5988i 1.47437 0.689482i
\(809\) 2.99378i 0.105256i −0.998614 0.0526278i \(-0.983240\pi\)
0.998614 0.0526278i \(-0.0167597\pi\)
\(810\) −18.4856 + 14.6275i −0.649517 + 0.513958i
\(811\) −2.28628 2.28628i −0.0802820 0.0802820i 0.665825 0.746108i \(-0.268080\pi\)
−0.746108 + 0.665825i \(0.768080\pi\)
\(812\) −6.09616 9.86721i −0.213933 0.346271i
\(813\) 20.7839 20.7839i 0.728923 0.728923i
\(814\) −4.27497 0.498088i −0.149838 0.0174580i
\(815\) −34.4644 −1.20724
\(816\) 16.6417 5.54151i 0.582577 0.193992i
\(817\) 16.6454 0.582351
\(818\) 5.70817 + 0.665073i 0.199582 + 0.0232537i
\(819\) −6.13262 + 6.13262i −0.214291 + 0.214291i
\(820\) −48.9323 + 30.2313i −1.70879 + 1.05572i
\(821\) −28.6342 28.6342i −0.999339 0.999339i 0.000660747 1.00000i \(-0.499790\pi\)
−1.00000 0.000660747i \(0.999790\pi\)
\(822\) 73.0149 57.7761i 2.54669 2.01517i
\(823\) 41.0492i 1.43088i 0.698672 + 0.715442i \(0.253775\pi\)
−0.698672 + 0.715442i \(0.746225\pi\)
\(824\) 45.7001 + 16.5767i 1.59204 + 0.577476i
\(825\) 37.3437i 1.30014i
\(826\) 1.41284 + 1.78548i 0.0491590 + 0.0621249i
\(827\) −20.3987 20.3987i −0.709331 0.709331i 0.257064 0.966394i \(-0.417245\pi\)
−0.966394 + 0.257064i \(0.917245\pi\)
\(828\) 50.5666 + 11.9454i 1.75731 + 0.415132i
\(829\) −18.4892 + 18.4892i −0.642155 + 0.642155i −0.951085 0.308930i \(-0.900029\pi\)
0.308930 + 0.951085i \(0.400029\pi\)
\(830\) −6.39402 + 54.8784i −0.221940 + 1.90486i
\(831\) 45.2428 1.56945
\(832\) 12.6891 1.13822i 0.439916 0.0394608i
\(833\) 1.50885 0.0522786
\(834\) 4.47141 38.3771i 0.154832 1.32889i
\(835\) 32.2341 32.2341i 1.11551 1.11551i
\(836\) −5.23641 1.23701i −0.181105 0.0427828i
\(837\) 20.6591 + 20.6591i 0.714084 + 0.714084i
\(838\) −0.685352 0.866117i −0.0236751 0.0299195i
\(839\) 41.9862i 1.44953i −0.688999 0.724763i \(-0.741949\pi\)
0.688999 0.724763i \(-0.258051\pi\)
\(840\) 29.8082 + 10.8123i 1.02848 + 0.373059i
\(841\) 4.63123i 0.159698i
\(842\) −5.92474 + 4.68820i −0.204180 + 0.161566i
\(843\) 8.67205 + 8.67205i 0.298681 + 0.298681i
\(844\) −2.18456 + 1.34966i −0.0751956 + 0.0464573i
\(845\) −28.5421 + 28.5421i −0.981876 + 0.981876i
\(846\) −27.5210 3.20654i −0.946193 0.110243i
\(847\) 9.30861 0.319848
\(848\) −1.20763 3.62664i −0.0414701 0.124539i
\(849\) 68.1577 2.33916
\(850\) −20.9413 2.43992i −0.718281 0.0836886i
\(851\) −7.89326 + 7.89326i −0.270577 + 0.270577i
\(852\) −42.2207 68.3382i −1.44646 2.34123i
\(853\) 10.9845 + 10.9845i 0.376104 + 0.376104i 0.869694 0.493591i \(-0.164316\pi\)
−0.493591 + 0.869694i \(0.664316\pi\)
\(854\) −5.04831 + 3.99469i −0.172750 + 0.136695i
\(855\) 43.4570i 1.48620i
\(856\) −14.8610 + 6.94968i −0.507939 + 0.237535i
\(857\) 47.3215i 1.61647i 0.588858 + 0.808237i \(0.299578\pi\)
−0.588858 + 0.808237i \(0.700422\pi\)
\(858\) −5.28204 6.67520i −0.180326 0.227888i
\(859\) 5.11128 + 5.11128i 0.174395 + 0.174395i 0.788907 0.614512i \(-0.210647\pi\)
−0.614512 + 0.788907i \(0.710647\pi\)
\(860\) 14.2726 60.4178i 0.486692 2.06023i
\(861\) −15.3207 + 15.3207i −0.522127 + 0.522127i
\(862\) 0.193431 1.66017i 0.00658828 0.0565458i
\(863\) 10.1105 0.344167 0.172084 0.985082i \(-0.444950\pi\)
0.172084 + 0.985082i \(0.444950\pi\)
\(864\) 39.3668 8.20369i 1.33929 0.279095i
\(865\) 30.7603 1.04588
\(866\) −2.49729 + 21.4337i −0.0848614 + 0.728346i
\(867\) 30.2565 30.2565i 1.02756 1.02756i
\(868\) 1.88981 7.99980i 0.0641442 0.271531i
\(869\) −1.63656 1.63656i −0.0555165 0.0555165i
\(870\) 57.0526 + 72.1006i 1.93427 + 2.44444i
\(871\) 3.43769i 0.116482i
\(872\) −5.54680 11.8611i −0.187838 0.401669i
\(873\) 88.3493i 2.99017i
\(874\) −10.9435 + 8.65950i −0.370169 + 0.292912i
\(875\) −13.3118 13.3118i −0.450021 0.450021i
\(876\) 44.2207 + 71.5754i 1.49408 + 2.41831i
\(877\) −38.0640 + 38.0640i −1.28533 + 1.28533i −0.347738 + 0.937592i \(0.613050\pi\)
−0.937592 + 0.347738i \(0.886950\pi\)
\(878\) 6.10350 + 0.711133i 0.205983 + 0.0239996i
\(879\) 55.5844 1.87482
\(880\) −8.97990 + 17.9459i −0.302712 + 0.604955i
\(881\) −21.5769 −0.726946 −0.363473 0.931605i \(-0.618409\pi\)
−0.363473 + 0.931605i \(0.618409\pi\)
\(882\) 7.65008 + 0.891330i 0.257592 + 0.0300126i
\(883\) 21.5700 21.5700i 0.725888 0.725888i −0.243910 0.969798i \(-0.578430\pi\)
0.969798 + 0.243910i \(0.0784300\pi\)
\(884\) −4.08838 + 2.52588i −0.137507 + 0.0849546i
\(885\) −12.7625 12.7625i −0.429008 0.429008i
\(886\) −6.76586 + 5.35377i −0.227303 + 0.179863i
\(887\) 33.7110i 1.13191i 0.824437 + 0.565953i \(0.191492\pi\)
−0.824437 + 0.565953i \(0.808508\pi\)
\(888\) −6.55898 + 18.0824i −0.220105 + 0.606804i
\(889\) 12.9787i 0.435291i
\(890\) 28.6350 + 36.1876i 0.959846 + 1.21301i
\(891\) −3.97372 3.97372i −0.133125 0.133125i
\(892\) 6.23476 + 1.47285i 0.208755 + 0.0493146i
\(893\) 5.26208 5.26208i 0.176089 0.176089i
\(894\) −5.22683 + 44.8607i −0.174811 + 1.50037i
\(895\) 63.9788 2.13858
\(896\) −7.78499 8.20939i −0.260078 0.274256i
\(897\) −22.0777 −0.737153
\(898\) 0.609656 5.23254i 0.0203445 0.174612i
\(899\) 16.8538 16.8538i 0.562105 0.562105i
\(900\) −104.734 24.7415i −3.49113 0.824716i
\(901\) 1.01955 + 1.01955i 0.0339662 + 0.0339662i
\(902\) −8.50865 10.7529i −0.283307 0.358031i
\(903\) 23.3855i 0.778222i
\(904\) 8.84597 24.3873i 0.294213 0.811111i
\(905\) 22.8346i 0.759047i
\(906\) −17.6244 + 13.9460i −0.585530 + 0.463326i
\(907\) 0.923962 + 0.923962i 0.0306797 + 0.0306797i 0.722280 0.691601i \(-0.243094\pi\)
−0.691601 + 0.722280i \(0.743094\pi\)
\(908\) 33.1894 20.5051i 1.10143 0.680485i
\(909\) −62.9911 + 62.9911i −2.08928 + 2.08928i
\(910\) −8.62928 1.00542i −0.286058 0.0333293i
\(911\) −29.9873 −0.993522 −0.496761 0.867887i \(-0.665477\pi\)
−0.496761 + 0.867887i \(0.665477\pi\)
\(912\) −10.7608 + 21.5049i −0.356326 + 0.712099i
\(913\) −13.1713 −0.435908
\(914\) 15.0938 + 1.75862i 0.499259 + 0.0581699i
\(915\) 36.0851 36.0851i 1.19294 1.19294i
\(916\) −10.4387 16.8960i −0.344904 0.558261i
\(917\) −6.81965 6.81965i −0.225205 0.225205i
\(918\) −11.8951 + 9.41250i −0.392597 + 0.310659i
\(919\) 13.0725i 0.431220i 0.976480 + 0.215610i \(0.0691741\pi\)
−0.976480 + 0.215610i \(0.930826\pi\)
\(920\) 22.0478 + 47.1466i 0.726896 + 1.55438i
\(921\) 36.7182i 1.20991i
\(922\) −9.78917 12.3711i −0.322389 0.407421i
\(923\) 15.5626 + 15.5626i 0.512248 + 0.512248i
\(924\) −1.73790 + 7.35674i −0.0571726 + 0.242019i
\(925\) 16.3486 16.3486i 0.537538 0.537538i
\(926\) 4.47603 38.4167i 0.147091 1.26245i
\(927\) −93.6035 −3.07434
\(928\) −6.69260 32.1156i −0.219695 1.05424i
\(929\) −20.7057 −0.679333 −0.339667 0.940546i \(-0.610314\pi\)
−0.339667 + 0.940546i \(0.610314\pi\)
\(930\) −7.54106 + 64.7232i −0.247281 + 2.12236i
\(931\) −1.46271 + 1.46271i −0.0479385 + 0.0479385i
\(932\) 1.35118 5.71971i 0.0442593 0.187355i
\(933\) −40.6348 40.6348i −1.33033 1.33033i
\(934\) −14.1373 17.8661i −0.462588 0.584598i
\(935\) 7.56961i 0.247553i
\(936\) −22.2208 + 10.3914i −0.726308 + 0.339654i
\(937\) 5.93799i 0.193986i 0.995285 + 0.0969929i \(0.0309224\pi\)
−0.995285 + 0.0969929i \(0.969078\pi\)
\(938\) −2.39398 + 1.89434i −0.0781661 + 0.0618523i
\(939\) −17.9348 17.9348i −0.585281 0.585281i
\(940\) −14.5878 23.6117i −0.475801 0.770129i
\(941\) −13.9955 + 13.9955i −0.456241 + 0.456241i −0.897419 0.441178i \(-0.854561\pi\)
0.441178 + 0.897419i \(0.354561\pi\)
\(942\) −32.4302 3.77852i −1.05663 0.123111i
\(943\) −35.5642 −1.15813
\(944\) 2.03459 + 6.11007i 0.0662201 + 0.198866i
\(945\) −27.4215 −0.892023
\(946\) 14.7004 + 1.71278i 0.477952 + 0.0556873i
\(947\) −30.2690 + 30.2690i −0.983611 + 0.983611i −0.999868 0.0162570i \(-0.994825\pi\)
0.0162570 + 0.999868i \(0.494825\pi\)
\(948\) −8.79984 + 5.43671i −0.285805 + 0.176576i
\(949\) −16.2998 16.2998i −0.529113 0.529113i
\(950\) 22.6663 17.9356i 0.735391 0.581909i
\(951\) 78.1710i 2.53487i
\(952\) 4.01190 + 1.45523i 0.130027 + 0.0471643i
\(953\) 0.689500i 0.0223351i −0.999938 0.0111675i \(-0.996445\pi\)
0.999938 0.0111675i \(-0.00355481\pi\)
\(954\) 4.56699 + 5.77155i 0.147862 + 0.186861i
\(955\) 33.7348 + 33.7348i 1.09163 + 1.09163i
\(956\) −31.5533 7.45388i −1.02051 0.241076i
\(957\) −15.4990 + 15.4990i −0.501012 + 0.501012i
\(958\) 1.86383 15.9968i 0.0602176 0.516834i
\(959\) 22.6543 0.731544
\(960\) 68.8294 + 57.4977i 2.22146 + 1.85573i
\(961\) −14.1080 −0.455096
\(962\) 0.609910 5.23472i 0.0196643 0.168774i
\(963\) 22.3365 22.3365i 0.719783 0.719783i
\(964\) 27.4769 + 6.49092i 0.884971 + 0.209058i
\(965\) 64.6012 + 64.6012i 2.07959 + 2.07959i
\(966\) 12.1659 + 15.3747i 0.391432 + 0.494674i
\(967\) 14.1022i 0.453497i 0.973953 + 0.226749i \(0.0728096\pi\)
−0.973953 + 0.226749i \(0.927190\pi\)
\(968\) 24.7508 + 8.97780i 0.795520 + 0.288557i
\(969\) 9.07083i 0.291397i
\(970\) 69.4010 54.9164i 2.22833 1.76326i
\(971\) −0.255230 0.255230i −0.00819071 0.00819071i 0.703000 0.711190i \(-0.251844\pi\)
−0.711190 + 0.703000i \(0.751844\pi\)
\(972\) 14.9184 9.21689i 0.478508 0.295632i
\(973\) 6.64728 6.64728i 0.213102 0.213102i
\(974\) −44.0421 5.13145i −1.41120 0.164422i
\(975\) 45.7275 1.46445
\(976\) −17.2757 + 5.75263i −0.552983 + 0.184137i
\(977\) −9.83910 −0.314781 −0.157390 0.987536i \(-0.550308\pi\)
−0.157390 + 0.987536i \(0.550308\pi\)
\(978\) −36.4736 4.24963i −1.16630 0.135888i
\(979\) −7.77902 + 7.77902i −0.248618 + 0.248618i
\(980\) 4.05500 + 6.56340i 0.129532 + 0.209660i
\(981\) 17.8276 + 17.8276i 0.569191 + 0.569191i
\(982\) 31.8028 25.1653i 1.01487 0.803057i
\(983\) 26.6489i 0.849968i −0.905201 0.424984i \(-0.860280\pi\)
0.905201 0.424984i \(-0.139720\pi\)
\(984\) −55.5125 + 25.9601i −1.76967 + 0.827578i
\(985\) 62.2971i 1.98495i
\(986\) 7.67875 + 9.70406i 0.244541 + 0.309040i
\(987\) −7.39281 7.39281i −0.235316 0.235316i
\(988\) 1.51472 6.41201i 0.0481896 0.203993i
\(989\) 27.1427 27.1427i 0.863086 0.863086i
\(990\) 4.47163 38.3790i 0.142118 1.21976i
\(991\) 16.8287 0.534583 0.267291 0.963616i \(-0.413871\pi\)
0.267291 + 0.963616i \(0.413871\pi\)
\(992\) 12.7403 19.4481i 0.404506 0.617478i
\(993\) −91.7875 −2.91279
\(994\) 2.26190 19.4134i 0.0717432 0.615756i
\(995\) −14.9935 + 14.9935i −0.475326 + 0.475326i
\(996\) −13.5335 + 57.2892i −0.428826 + 1.81528i
\(997\) −25.7816 25.7816i −0.816511 0.816511i 0.169089 0.985601i \(-0.445917\pi\)
−0.985601 + 0.169089i \(0.945917\pi\)
\(998\) 22.9800 + 29.0412i 0.727421 + 0.919282i
\(999\) 16.6346i 0.526294i
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 112.2.m.d.85.3 yes 12
4.3 odd 2 448.2.m.d.113.6 12
7.2 even 3 784.2.x.l.165.2 24
7.3 odd 6 784.2.x.m.373.5 24
7.4 even 3 784.2.x.l.373.5 24
7.5 odd 6 784.2.x.m.165.2 24
7.6 odd 2 784.2.m.h.197.3 12
8.3 odd 2 896.2.m.h.225.1 12
8.5 even 2 896.2.m.g.225.6 12
16.3 odd 4 448.2.m.d.337.6 12
16.5 even 4 896.2.m.g.673.6 12
16.11 odd 4 896.2.m.h.673.1 12
16.13 even 4 inner 112.2.m.d.29.3 12
32.3 odd 8 7168.2.a.bi.1.11 12
32.13 even 8 7168.2.a.bj.1.11 12
32.19 odd 8 7168.2.a.bi.1.2 12
32.29 even 8 7168.2.a.bj.1.2 12
112.13 odd 4 784.2.m.h.589.3 12
112.45 odd 12 784.2.x.m.765.2 24
112.61 odd 12 784.2.x.m.557.5 24
112.93 even 12 784.2.x.l.557.5 24
112.109 even 12 784.2.x.l.765.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.d.29.3 12 16.13 even 4 inner
112.2.m.d.85.3 yes 12 1.1 even 1 trivial
448.2.m.d.113.6 12 4.3 odd 2
448.2.m.d.337.6 12 16.3 odd 4
784.2.m.h.197.3 12 7.6 odd 2
784.2.m.h.589.3 12 112.13 odd 4
784.2.x.l.165.2 24 7.2 even 3
784.2.x.l.373.5 24 7.4 even 3
784.2.x.l.557.5 24 112.93 even 12
784.2.x.l.765.2 24 112.109 even 12
784.2.x.m.165.2 24 7.5 odd 6
784.2.x.m.373.5 24 7.3 odd 6
784.2.x.m.557.5 24 112.61 odd 12
784.2.x.m.765.2 24 112.45 odd 12
896.2.m.g.225.6 12 8.5 even 2
896.2.m.g.673.6 12 16.5 even 4
896.2.m.h.225.1 12 8.3 odd 2
896.2.m.h.673.1 12 16.11 odd 4
7168.2.a.bi.1.2 12 32.19 odd 8
7168.2.a.bi.1.11 12 32.3 odd 8
7168.2.a.bj.1.2 12 32.29 even 8
7168.2.a.bj.1.11 12 32.13 even 8