Properties

Label 784.2.x.o.165.2
Level $784$
Weight $2$
Character 784.165
Analytic conductor $6.260$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 165.2
Character \(\chi\) \(=\) 784.165
Dual form 784.2.x.o.765.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32577 - 0.492271i) q^{2} +(0.221819 + 0.827840i) q^{3} +(1.51534 + 1.30528i) q^{4} +(1.10095 - 4.10878i) q^{5} +(0.113440 - 1.20672i) q^{6} +(-1.36644 - 2.47646i) q^{8} +(1.96196 - 1.13274i) q^{9} +O(q^{10})\) \(q+(-1.32577 - 0.492271i) q^{2} +(0.221819 + 0.827840i) q^{3} +(1.51534 + 1.30528i) q^{4} +(1.10095 - 4.10878i) q^{5} +(0.113440 - 1.20672i) q^{6} +(-1.36644 - 2.47646i) q^{8} +(1.96196 - 1.13274i) q^{9} +(-3.48224 + 4.90534i) q^{10} +(1.18894 - 0.318576i) q^{11} +(-0.744430 + 1.54399i) q^{12} +(1.73092 - 1.73092i) q^{13} +3.64563 q^{15} +(0.592502 + 3.95587i) q^{16} +(0.931914 - 1.61412i) q^{17} +(-3.15872 + 0.535936i) q^{18} +(-3.69400 - 0.989804i) q^{19} +(7.03141 - 4.78916i) q^{20} +(-1.73309 - 0.162922i) q^{22} +(-1.23305 + 0.711901i) q^{23} +(1.74701 - 1.68052i) q^{24} +(-11.3399 - 6.54709i) q^{25} +(-3.14688 + 1.44272i) q^{26} +(3.19099 + 3.19099i) q^{27} +(-0.181826 + 0.181826i) q^{29} +(-4.83327 - 1.79464i) q^{30} +(-3.23200 + 5.59799i) q^{31} +(1.16184 - 5.53626i) q^{32} +(0.527459 + 0.913587i) q^{33} +(-2.03009 + 1.68120i) q^{34} +(4.45157 + 0.844420i) q^{36} +(-0.0637719 + 0.238000i) q^{37} +(4.41015 + 3.13070i) q^{38} +(1.81687 + 1.04897i) q^{39} +(-11.6796 + 2.88797i) q^{40} -0.440182i q^{41} +(-5.54503 - 5.54503i) q^{43} +(2.21748 + 1.06915i) q^{44} +(-2.49417 - 9.30835i) q^{45} +(1.98519 - 0.336824i) q^{46} +(3.61427 + 6.26009i) q^{47} +(-3.14340 + 1.36799i) q^{48} +(11.8112 + 14.2623i) q^{50} +(1.54295 + 0.413433i) q^{51} +(4.88225 - 0.363599i) q^{52} +(9.69274 - 2.59716i) q^{53} +(-2.65969 - 5.80136i) q^{54} -5.23583i q^{55} -3.27760i q^{57} +(0.330567 - 0.151552i) q^{58} +(-1.63688 + 0.438601i) q^{59} +(5.52436 + 4.75856i) q^{60} +(9.01647 + 2.41596i) q^{61} +(7.04063 - 5.83064i) q^{62} +(-4.26567 + 6.76787i) q^{64} +(-5.20632 - 9.01761i) q^{65} +(-0.249558 - 1.47086i) q^{66} +(-2.57076 - 9.59422i) q^{67} +(3.51904 - 1.22953i) q^{68} +(-0.862854 - 0.862854i) q^{69} -11.2912i q^{71} +(-5.48608 - 3.31089i) q^{72} +(-8.13092 - 4.69439i) q^{73} +(0.201707 - 0.284140i) q^{74} +(2.90454 - 10.8399i) q^{75} +(-4.30569 - 6.32158i) q^{76} +(-1.89238 - 2.28509i) q^{78} +(6.52948 + 11.3094i) q^{79} +(16.9061 + 1.92074i) q^{80} +(1.46441 - 2.53643i) q^{81} +(-0.216689 + 0.583580i) q^{82} +(3.06926 - 3.06926i) q^{83} +(-5.60609 - 5.60609i) q^{85} +(4.62178 + 10.0811i) q^{86} +(-0.190855 - 0.110190i) q^{87} +(-2.41356 - 2.50904i) q^{88} +(-5.66084 + 3.26829i) q^{89} +(-1.27554 + 13.5686i) q^{90} +(-2.79771 - 0.530699i) q^{92} +(-5.35117 - 1.43384i) q^{93} +(-1.71003 - 10.0786i) q^{94} +(-8.13378 + 14.0881i) q^{95} +(4.84085 - 0.266229i) q^{96} -1.70409 q^{97} +(1.97179 - 1.97179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32577 0.492271i −0.937462 0.348088i
\(3\) 0.221819 + 0.827840i 0.128067 + 0.477954i 0.999930 0.0117959i \(-0.00375483\pi\)
−0.871863 + 0.489750i \(0.837088\pi\)
\(4\) 1.51534 + 1.30528i 0.757669 + 0.652639i
\(5\) 1.10095 4.10878i 0.492358 1.83750i −0.0519945 0.998647i \(-0.516558\pi\)
0.544352 0.838857i \(-0.316775\pi\)
\(6\) 0.113440 1.20672i 0.0463118 0.492642i
\(7\) 0 0
\(8\) −1.36644 2.47646i −0.483110 0.875560i
\(9\) 1.96196 1.13274i 0.653987 0.377579i
\(10\) −3.48224 + 4.90534i −1.10118 + 1.55121i
\(11\) 1.18894 0.318576i 0.358479 0.0960542i −0.0750845 0.997177i \(-0.523923\pi\)
0.433564 + 0.901123i \(0.357256\pi\)
\(12\) −0.744430 + 1.54399i −0.214898 + 0.445713i
\(13\) 1.73092 1.73092i 0.480070 0.480070i −0.425084 0.905154i \(-0.639755\pi\)
0.905154 + 0.425084i \(0.139755\pi\)
\(14\) 0 0
\(15\) 3.64563 0.941297
\(16\) 0.592502 + 3.95587i 0.148125 + 0.988969i
\(17\) 0.931914 1.61412i 0.226022 0.391482i −0.730603 0.682802i \(-0.760761\pi\)
0.956626 + 0.291320i \(0.0940945\pi\)
\(18\) −3.15872 + 0.535936i −0.744519 + 0.126321i
\(19\) −3.69400 0.989804i −0.847462 0.227077i −0.191145 0.981562i \(-0.561220\pi\)
−0.656317 + 0.754485i \(0.727887\pi\)
\(20\) 7.03141 4.78916i 1.57227 1.07089i
\(21\) 0 0
\(22\) −1.73309 0.162922i −0.369496 0.0347352i
\(23\) −1.23305 + 0.711901i −0.257108 + 0.148442i −0.623015 0.782210i \(-0.714092\pi\)
0.365906 + 0.930652i \(0.380759\pi\)
\(24\) 1.74701 1.68052i 0.356606 0.343035i
\(25\) −11.3399 6.54709i −2.26798 1.30942i
\(26\) −3.14688 + 1.44272i −0.617154 + 0.282941i
\(27\) 3.19099 + 3.19099i 0.614106 + 0.614106i
\(28\) 0 0
\(29\) −0.181826 + 0.181826i −0.0337642 + 0.0337642i −0.723787 0.690023i \(-0.757600\pi\)
0.690023 + 0.723787i \(0.257600\pi\)
\(30\) −4.83327 1.79464i −0.882430 0.327654i
\(31\) −3.23200 + 5.59799i −0.580485 + 1.00543i 0.414937 + 0.909850i \(0.363804\pi\)
−0.995422 + 0.0955792i \(0.969530\pi\)
\(32\) 1.16184 5.53626i 0.205386 0.978681i
\(33\) 0.527459 + 0.913587i 0.0918189 + 0.159035i
\(34\) −2.03009 + 1.68120i −0.348157 + 0.288324i
\(35\) 0 0
\(36\) 4.45157 + 0.844420i 0.741929 + 0.140737i
\(37\) −0.0637719 + 0.238000i −0.0104840 + 0.0391269i −0.970970 0.239202i \(-0.923114\pi\)
0.960486 + 0.278329i \(0.0897807\pi\)
\(38\) 4.41015 + 3.13070i 0.715420 + 0.507867i
\(39\) 1.81687 + 1.04897i 0.290933 + 0.167970i
\(40\) −11.6796 + 2.88797i −1.84671 + 0.456628i
\(41\) 0.440182i 0.0687448i −0.999409 0.0343724i \(-0.989057\pi\)
0.999409 0.0343724i \(-0.0109432\pi\)
\(42\) 0 0
\(43\) −5.54503 5.54503i −0.845609 0.845609i 0.143972 0.989582i \(-0.454012\pi\)
−0.989582 + 0.143972i \(0.954012\pi\)
\(44\) 2.21748 + 1.06915i 0.334297 + 0.161180i
\(45\) −2.49417 9.30835i −0.371808 1.38761i
\(46\) 1.98519 0.336824i 0.292700 0.0496619i
\(47\) 3.61427 + 6.26009i 0.527195 + 0.913128i 0.999498 + 0.0316918i \(0.0100895\pi\)
−0.472303 + 0.881436i \(0.656577\pi\)
\(48\) −3.14340 + 1.36799i −0.453711 + 0.197452i
\(49\) 0 0
\(50\) 11.8112 + 14.2623i 1.67035 + 2.01699i
\(51\) 1.54295 + 0.413433i 0.216056 + 0.0578921i
\(52\) 4.88225 0.363599i 0.677047 0.0504220i
\(53\) 9.69274 2.59716i 1.33140 0.356747i 0.478163 0.878271i \(-0.341303\pi\)
0.853237 + 0.521524i \(0.174636\pi\)
\(54\) −2.65969 5.80136i −0.361938 0.789464i
\(55\) 5.23583i 0.706000i
\(56\) 0 0
\(57\) 3.27760i 0.434129i
\(58\) 0.330567 0.151552i 0.0434056 0.0198998i
\(59\) −1.63688 + 0.438601i −0.213104 + 0.0571010i −0.363791 0.931480i \(-0.618518\pi\)
0.150688 + 0.988581i \(0.451851\pi\)
\(60\) 5.52436 + 4.75856i 0.713192 + 0.614327i
\(61\) 9.01647 + 2.41596i 1.15444 + 0.309331i 0.784743 0.619821i \(-0.212795\pi\)
0.369697 + 0.929152i \(0.379461\pi\)
\(62\) 7.04063 5.83064i 0.894161 0.740492i
\(63\) 0 0
\(64\) −4.26567 + 6.76787i −0.533209 + 0.845984i
\(65\) −5.20632 9.01761i −0.645765 1.11850i
\(66\) −0.249558 1.47086i −0.0307185 0.181050i
\(67\) −2.57076 9.59422i −0.314069 1.17212i −0.924853 0.380324i \(-0.875813\pi\)
0.610785 0.791797i \(-0.290854\pi\)
\(68\) 3.51904 1.22953i 0.426746 0.149103i
\(69\) −0.862854 0.862854i −0.103875 0.103875i
\(70\) 0 0
\(71\) 11.2912i 1.34002i −0.742352 0.670010i \(-0.766290\pi\)
0.742352 0.670010i \(-0.233710\pi\)
\(72\) −5.48608 3.31089i −0.646541 0.390192i
\(73\) −8.13092 4.69439i −0.951652 0.549437i −0.0580583 0.998313i \(-0.518491\pi\)
−0.893594 + 0.448877i \(0.851824\pi\)
\(74\) 0.201707 0.284140i 0.0234480 0.0330306i
\(75\) 2.90454 10.8399i 0.335388 1.25168i
\(76\) −4.30569 6.32158i −0.493897 0.725135i
\(77\) 0 0
\(78\) −1.89238 2.28509i −0.214270 0.258736i
\(79\) 6.52948 + 11.3094i 0.734624 + 1.27241i 0.954888 + 0.296966i \(0.0959747\pi\)
−0.220264 + 0.975440i \(0.570692\pi\)
\(80\) 16.9061 + 1.92074i 1.89016 + 0.214745i
\(81\) 1.46441 2.53643i 0.162712 0.281825i
\(82\) −0.216689 + 0.583580i −0.0239293 + 0.0644456i
\(83\) 3.06926 3.06926i 0.336895 0.336895i −0.518302 0.855198i \(-0.673436\pi\)
0.855198 + 0.518302i \(0.173436\pi\)
\(84\) 0 0
\(85\) −5.60609 5.60609i −0.608066 0.608066i
\(86\) 4.62178 + 10.0811i 0.498380 + 1.08707i
\(87\) −0.190855 0.110190i −0.0204618 0.0118137i
\(88\) −2.41356 2.50904i −0.257286 0.267465i
\(89\) −5.66084 + 3.26829i −0.600047 + 0.346438i −0.769060 0.639176i \(-0.779275\pi\)
0.169013 + 0.985614i \(0.445942\pi\)
\(90\) −1.27554 + 13.5686i −0.134454 + 1.43025i
\(91\) 0 0
\(92\) −2.79771 0.530699i −0.291682 0.0553292i
\(93\) −5.35117 1.43384i −0.554890 0.148682i
\(94\) −1.71003 10.0786i −0.176376 1.03953i
\(95\) −8.13378 + 14.0881i −0.834508 + 1.44541i
\(96\) 4.84085 0.266229i 0.494068 0.0271719i
\(97\) −1.70409 −0.173024 −0.0865122 0.996251i \(-0.527572\pi\)
−0.0865122 + 0.996251i \(0.527572\pi\)
\(98\) 0 0
\(99\) 1.97179 1.97179i 0.198172 0.198172i
\(100\) −8.63801 24.7228i −0.863801 2.47228i
\(101\) 2.36178 0.632838i 0.235006 0.0629697i −0.139394 0.990237i \(-0.544515\pi\)
0.374400 + 0.927267i \(0.377849\pi\)
\(102\) −1.84208 1.30767i −0.182393 0.129478i
\(103\) 12.6328 7.29353i 1.24474 0.718653i 0.274687 0.961534i \(-0.411426\pi\)
0.970056 + 0.242881i \(0.0780923\pi\)
\(104\) −6.65174 1.92134i −0.652257 0.188403i
\(105\) 0 0
\(106\) −14.1289 1.32821i −1.37232 0.129007i
\(107\) 1.28684 4.80256i 0.124404 0.464281i −0.875414 0.483374i \(-0.839411\pi\)
0.999818 + 0.0190927i \(0.00607777\pi\)
\(108\) 0.670303 + 9.00056i 0.0644999 + 0.866079i
\(109\) 2.61683 + 9.76613i 0.250647 + 0.935426i 0.970461 + 0.241259i \(0.0775604\pi\)
−0.719814 + 0.694167i \(0.755773\pi\)
\(110\) −2.57745 + 6.94152i −0.245750 + 0.661848i
\(111\) −0.211172 −0.0200435
\(112\) 0 0
\(113\) 5.22780 0.491791 0.245895 0.969296i \(-0.420918\pi\)
0.245895 + 0.969296i \(0.420918\pi\)
\(114\) −1.61347 + 4.34535i −0.151115 + 0.406979i
\(115\) 1.56753 + 5.85009i 0.146173 + 0.545524i
\(116\) −0.512861 + 0.0381946i −0.0476180 + 0.00354628i
\(117\) 1.43532 5.35667i 0.132695 0.495224i
\(118\) 2.38604 + 0.224305i 0.219653 + 0.0206489i
\(119\) 0 0
\(120\) −4.98154 9.02824i −0.454750 0.824162i
\(121\) −8.21419 + 4.74247i −0.746745 + 0.431133i
\(122\) −10.7645 7.64155i −0.974569 0.691834i
\(123\) 0.364400 0.0976407i 0.0328568 0.00880396i
\(124\) −12.2045 + 4.26420i −1.09600 + 0.382936i
\(125\) −24.3460 + 24.3460i −2.17757 + 2.17757i
\(126\) 0 0
\(127\) −1.20463 −0.106893 −0.0534467 0.998571i \(-0.517021\pi\)
−0.0534467 + 0.998571i \(0.517021\pi\)
\(128\) 8.98693 6.87278i 0.794340 0.607473i
\(129\) 3.36041 5.82039i 0.295867 0.512457i
\(130\) 2.46328 + 14.5182i 0.216044 + 1.27333i
\(131\) −3.02113 0.809509i −0.263957 0.0707272i 0.124413 0.992231i \(-0.460295\pi\)
−0.388370 + 0.921503i \(0.626962\pi\)
\(132\) −0.393204 + 2.07287i −0.0342240 + 0.180421i
\(133\) 0 0
\(134\) −1.31471 + 13.9853i −0.113574 + 1.20814i
\(135\) 16.6242 9.59798i 1.43078 0.826063i
\(136\) −5.27071 0.102240i −0.451959 0.00876698i
\(137\) −0.286357 0.165329i −0.0244652 0.0141250i 0.487718 0.873001i \(-0.337830\pi\)
−0.512183 + 0.858877i \(0.671163\pi\)
\(138\) 0.719189 + 1.56870i 0.0612214 + 0.133537i
\(139\) 2.41295 + 2.41295i 0.204663 + 0.204663i 0.801995 0.597331i \(-0.203772\pi\)
−0.597331 + 0.801995i \(0.703772\pi\)
\(140\) 0 0
\(141\) −4.38064 + 4.38064i −0.368917 + 0.368917i
\(142\) −5.55834 + 14.9696i −0.466445 + 1.25622i
\(143\) 1.50653 2.60939i 0.125982 0.218208i
\(144\) 5.64344 + 7.09012i 0.470286 + 0.590843i
\(145\) 0.546903 + 0.947264i 0.0454179 + 0.0786660i
\(146\) 8.46883 + 10.2263i 0.700885 + 0.846335i
\(147\) 0 0
\(148\) −0.407292 + 0.277410i −0.0334792 + 0.0228030i
\(149\) 0.633381 2.36381i 0.0518886 0.193651i −0.935116 0.354341i \(-0.884705\pi\)
0.987005 + 0.160690i \(0.0513719\pi\)
\(150\) −9.18692 + 12.9414i −0.750109 + 1.05666i
\(151\) −11.4320 6.60029i −0.930326 0.537124i −0.0434110 0.999057i \(-0.513823\pi\)
−0.886915 + 0.461934i \(0.847156\pi\)
\(152\) 2.59643 + 10.5005i 0.210598 + 0.851706i
\(153\) 4.22246i 0.341365i
\(154\) 0 0
\(155\) 19.4427 + 19.4427i 1.56167 + 1.56167i
\(156\) 1.38398 + 3.96107i 0.110807 + 0.317140i
\(157\) −0.925585 3.45433i −0.0738697 0.275685i 0.919105 0.394013i \(-0.128913\pi\)
−0.992975 + 0.118327i \(0.962247\pi\)
\(158\) −3.08931 18.2079i −0.245772 1.44855i
\(159\) 4.30007 + 7.44794i 0.341018 + 0.590660i
\(160\) −21.4682 10.8689i −1.69721 0.859259i
\(161\) 0 0
\(162\) −3.19008 + 2.64184i −0.250636 + 0.207562i
\(163\) 10.8521 + 2.90781i 0.850001 + 0.227757i 0.657420 0.753524i \(-0.271648\pi\)
0.192581 + 0.981281i \(0.438314\pi\)
\(164\) 0.574559 0.667024i 0.0448655 0.0520858i
\(165\) 4.33443 1.16141i 0.337435 0.0904155i
\(166\) −5.58005 + 2.55823i −0.433096 + 0.198557i
\(167\) 11.7171i 0.906693i −0.891334 0.453346i \(-0.850230\pi\)
0.891334 0.453346i \(-0.149770\pi\)
\(168\) 0 0
\(169\) 7.00785i 0.539065i
\(170\) 4.67268 + 10.1921i 0.358378 + 0.781699i
\(171\) −8.36867 + 2.24238i −0.639968 + 0.171479i
\(172\) −1.16480 15.6404i −0.0888148 1.19257i
\(173\) 10.5772 + 2.83415i 0.804169 + 0.215476i 0.637413 0.770522i \(-0.280004\pi\)
0.166755 + 0.985998i \(0.446671\pi\)
\(174\) 0.198787 + 0.240040i 0.0150700 + 0.0181974i
\(175\) 0 0
\(176\) 1.96469 + 4.51454i 0.148094 + 0.340296i
\(177\) −0.726183 1.25779i −0.0545833 0.0945410i
\(178\) 9.11386 1.54633i 0.683112 0.115903i
\(179\) 4.32641 + 16.1464i 0.323371 + 1.20684i 0.915939 + 0.401317i \(0.131447\pi\)
−0.592568 + 0.805520i \(0.701886\pi\)
\(180\) 8.37048 17.3609i 0.623899 1.29400i
\(181\) 15.9791 + 15.9791i 1.18772 + 1.18772i 0.977696 + 0.210025i \(0.0673544\pi\)
0.210025 + 0.977696i \(0.432646\pi\)
\(182\) 0 0
\(183\) 8.00010i 0.591385i
\(184\) 3.44788 + 2.08082i 0.254181 + 0.153400i
\(185\) 0.907680 + 0.524050i 0.0667340 + 0.0385289i
\(186\) 6.38858 + 4.53517i 0.468434 + 0.332535i
\(187\) 0.593770 2.21598i 0.0434208 0.162048i
\(188\) −2.69432 + 14.2038i −0.196503 + 1.03592i
\(189\) 0 0
\(190\) 17.7187 14.6736i 1.28545 1.06454i
\(191\) 4.97963 + 8.62497i 0.360313 + 0.624081i 0.988012 0.154375i \(-0.0493364\pi\)
−0.627699 + 0.778456i \(0.716003\pi\)
\(192\) −6.54892 2.03005i −0.472628 0.146506i
\(193\) −4.02312 + 6.96824i −0.289590 + 0.501585i −0.973712 0.227783i \(-0.926852\pi\)
0.684122 + 0.729368i \(0.260186\pi\)
\(194\) 2.25924 + 0.838876i 0.162204 + 0.0602278i
\(195\) 6.31028 6.31028i 0.451889 0.451889i
\(196\) 0 0
\(197\) 6.01951 + 6.01951i 0.428873 + 0.428873i 0.888244 0.459372i \(-0.151925\pi\)
−0.459372 + 0.888244i \(0.651925\pi\)
\(198\) −3.58480 + 1.64349i −0.254761 + 0.116798i
\(199\) 12.7812 + 7.37922i 0.906035 + 0.523099i 0.879153 0.476539i \(-0.158109\pi\)
0.0268814 + 0.999639i \(0.491442\pi\)
\(200\) −0.718278 + 37.0290i −0.0507899 + 2.61834i
\(201\) 7.37224 4.25636i 0.519998 0.300221i
\(202\) −3.44271 0.323639i −0.242228 0.0227712i
\(203\) 0 0
\(204\) 1.79845 + 2.64047i 0.125917 + 0.184870i
\(205\) −1.80861 0.484616i −0.126319 0.0338470i
\(206\) −20.3386 + 3.45081i −1.41705 + 0.240429i
\(207\) −1.61279 + 2.79344i −0.112097 + 0.194158i
\(208\) 7.87286 + 5.82172i 0.545885 + 0.403664i
\(209\) −4.70727 −0.325609
\(210\) 0 0
\(211\) 14.5016 14.5016i 0.998329 0.998329i −0.00166940 0.999999i \(-0.500531\pi\)
0.999999 + 0.00166940i \(0.000531387\pi\)
\(212\) 18.0778 + 8.71613i 1.24159 + 0.598626i
\(213\) 9.34732 2.50461i 0.640468 0.171613i
\(214\) −4.07022 + 5.73363i −0.278235 + 0.391943i
\(215\) −28.8881 + 16.6786i −1.97015 + 1.13747i
\(216\) 3.54205 12.2627i 0.241006 0.834368i
\(217\) 0 0
\(218\) 1.33827 14.2358i 0.0906391 0.964173i
\(219\) 2.08261 7.77241i 0.140730 0.525211i
\(220\) 6.83422 7.93406i 0.460763 0.534914i
\(221\) −1.18085 4.40698i −0.0794323 0.296445i
\(222\) 0.279965 + 0.103954i 0.0187900 + 0.00697691i
\(223\) −4.72461 −0.316383 −0.158192 0.987408i \(-0.550566\pi\)
−0.158192 + 0.987408i \(0.550566\pi\)
\(224\) 0 0
\(225\) −29.6646 −1.97764
\(226\) −6.93087 2.57350i −0.461035 0.171186i
\(227\) 4.26257 + 15.9081i 0.282917 + 1.05586i 0.950348 + 0.311189i \(0.100727\pi\)
−0.667431 + 0.744671i \(0.732606\pi\)
\(228\) 4.27818 4.96667i 0.283329 0.328926i
\(229\) −3.56601 + 13.3085i −0.235649 + 0.879453i 0.742207 + 0.670171i \(0.233779\pi\)
−0.977855 + 0.209282i \(0.932887\pi\)
\(230\) 0.801648 8.52753i 0.0528591 0.562289i
\(231\) 0 0
\(232\) 0.698739 + 0.201830i 0.0458745 + 0.0132508i
\(233\) −12.0806 + 6.97475i −0.791428 + 0.456931i −0.840465 0.541866i \(-0.817718\pi\)
0.0490370 + 0.998797i \(0.484385\pi\)
\(234\) −4.53983 + 6.39515i −0.296778 + 0.418064i
\(235\) 29.7005 7.95822i 1.93745 0.519137i
\(236\) −3.05293 1.47196i −0.198729 0.0958161i
\(237\) −7.91401 + 7.91401i −0.514070 + 0.514070i
\(238\) 0 0
\(239\) −23.1794 −1.49935 −0.749674 0.661807i \(-0.769790\pi\)
−0.749674 + 0.661807i \(0.769790\pi\)
\(240\) 2.16004 + 14.4216i 0.139430 + 0.930913i
\(241\) −2.09690 + 3.63195i −0.135073 + 0.233954i −0.925626 0.378441i \(-0.876460\pi\)
0.790552 + 0.612395i \(0.209794\pi\)
\(242\) 13.2247 2.24382i 0.850117 0.144238i
\(243\) 15.5015 + 4.15362i 0.994422 + 0.266455i
\(244\) 10.5095 + 15.4300i 0.672803 + 0.987804i
\(245\) 0 0
\(246\) −0.531177 0.0499343i −0.0338666 0.00318370i
\(247\) −8.10728 + 4.68074i −0.515854 + 0.297828i
\(248\) 18.2795 + 0.354581i 1.16075 + 0.0225159i
\(249\) 3.22168 + 1.86004i 0.204166 + 0.117875i
\(250\) 44.2621 20.2924i 2.79938 1.28340i
\(251\) 16.5937 + 16.5937i 1.04739 + 1.04739i 0.998820 + 0.0485679i \(0.0154657\pi\)
0.0485679 + 0.998820i \(0.484534\pi\)
\(252\) 0 0
\(253\) −1.23923 + 1.23923i −0.0779095 + 0.0779095i
\(254\) 1.59706 + 0.593003i 0.100208 + 0.0372083i
\(255\) 3.39741 5.88449i 0.212754 0.368501i
\(256\) −15.2979 + 4.68773i −0.956118 + 0.292983i
\(257\) −5.52727 9.57351i −0.344782 0.597179i 0.640532 0.767931i \(-0.278714\pi\)
−0.985314 + 0.170752i \(0.945380\pi\)
\(258\) −7.32034 + 6.06228i −0.455745 + 0.377421i
\(259\) 0 0
\(260\) 3.88115 20.4604i 0.240699 1.26890i
\(261\) −0.150774 + 0.562697i −0.00933269 + 0.0348301i
\(262\) 3.60683 + 2.56044i 0.222831 + 0.158184i
\(263\) 14.1936 + 8.19466i 0.875213 + 0.505304i 0.869077 0.494677i \(-0.164714\pi\)
0.00613562 + 0.999981i \(0.498047\pi\)
\(264\) 1.54171 2.55459i 0.0948860 0.157224i
\(265\) 42.6847i 2.62210i
\(266\) 0 0
\(267\) −3.96130 3.96130i −0.242428 0.242428i
\(268\) 8.62754 17.8941i 0.527011 1.09305i
\(269\) −0.333581 1.24494i −0.0203388 0.0759055i 0.955011 0.296572i \(-0.0958435\pi\)
−0.975349 + 0.220666i \(0.929177\pi\)
\(270\) −26.7647 + 4.54112i −1.62885 + 0.276364i
\(271\) −10.0688 17.4397i −0.611639 1.05939i −0.990964 0.134126i \(-0.957177\pi\)
0.379326 0.925263i \(-0.376156\pi\)
\(272\) 6.93742 + 2.73016i 0.420643 + 0.165540i
\(273\) 0 0
\(274\) 0.298258 + 0.360153i 0.0180184 + 0.0217577i
\(275\) −15.5682 4.17149i −0.938798 0.251550i
\(276\) −0.181252 2.43378i −0.0109101 0.146496i
\(277\) −31.1769 + 8.35382i −1.87324 + 0.501932i −0.873346 + 0.487100i \(0.838055\pi\)
−0.999890 + 0.0148319i \(0.995279\pi\)
\(278\) −2.01119 4.38684i −0.120623 0.263105i
\(279\) 14.6441i 0.876717i
\(280\) 0 0
\(281\) 13.6466i 0.814089i −0.913408 0.407044i \(-0.866559\pi\)
0.913408 0.407044i \(-0.133441\pi\)
\(282\) 7.96419 3.65127i 0.474261 0.217430i
\(283\) −18.1492 + 4.86306i −1.07886 + 0.289079i −0.754128 0.656728i \(-0.771940\pi\)
−0.324730 + 0.945807i \(0.605273\pi\)
\(284\) 14.7382 17.1100i 0.874549 1.01529i
\(285\) −13.4669 3.60846i −0.797713 0.213747i
\(286\) −3.28184 + 2.71783i −0.194059 + 0.160709i
\(287\) 0 0
\(288\) −3.99164 12.1780i −0.235210 0.717594i
\(289\) 6.76307 + 11.7140i 0.397828 + 0.689058i
\(290\) −0.258758 1.52508i −0.0151948 0.0895558i
\(291\) −0.378000 1.41072i −0.0221588 0.0826977i
\(292\) −6.19362 17.7267i −0.362454 1.03738i
\(293\) −2.19433 2.19433i −0.128194 0.128194i 0.640099 0.768293i \(-0.278893\pi\)
−0.768293 + 0.640099i \(0.778893\pi\)
\(294\) 0 0
\(295\) 7.20847i 0.419693i
\(296\) 0.676537 0.167285i 0.0393229 0.00972323i
\(297\) 4.81047 + 2.77733i 0.279132 + 0.161157i
\(298\) −2.00335 + 2.82208i −0.116051 + 0.163478i
\(299\) −0.902063 + 3.36655i −0.0521677 + 0.194692i
\(300\) 18.5504 12.6349i 1.07101 0.729475i
\(301\) 0 0
\(302\) 11.9071 + 14.3781i 0.685178 + 0.827368i
\(303\) 1.04778 + 1.81480i 0.0601932 + 0.104258i
\(304\) 1.72684 15.1995i 0.0990410 0.871749i
\(305\) 19.8533 34.3869i 1.13680 1.96899i
\(306\) −2.07859 + 5.59801i −0.118825 + 0.320017i
\(307\) 8.28029 8.28029i 0.472581 0.472581i −0.430168 0.902749i \(-0.641546\pi\)
0.902749 + 0.430168i \(0.141546\pi\)
\(308\) 0 0
\(309\) 8.84007 + 8.84007i 0.502894 + 0.502894i
\(310\) −16.2055 35.3476i −0.920410 2.00761i
\(311\) −7.36500 4.25218i −0.417631 0.241119i 0.276432 0.961033i \(-0.410848\pi\)
−0.694063 + 0.719914i \(0.744181\pi\)
\(312\) 0.115082 5.93277i 0.00651525 0.335877i
\(313\) −14.1001 + 8.14069i −0.796984 + 0.460139i −0.842415 0.538829i \(-0.818867\pi\)
0.0454317 + 0.998967i \(0.485534\pi\)
\(314\) −0.473353 + 5.03529i −0.0267128 + 0.284158i
\(315\) 0 0
\(316\) −4.86752 + 25.6603i −0.273819 + 1.44351i
\(317\) 21.8574 + 5.85666i 1.22763 + 0.328943i 0.813657 0.581345i \(-0.197474\pi\)
0.413975 + 0.910288i \(0.364140\pi\)
\(318\) −2.03450 11.9911i −0.114089 0.672425i
\(319\) −0.158255 + 0.274106i −0.00886058 + 0.0153470i
\(320\) 23.1114 + 24.9778i 1.29197 + 1.39630i
\(321\) 4.26120 0.237837
\(322\) 0 0
\(323\) −5.04015 + 5.04015i −0.280442 + 0.280442i
\(324\) 5.52982 1.93209i 0.307212 0.107338i
\(325\) −30.9609 + 8.29595i −1.71740 + 0.460177i
\(326\) −12.9560 9.19726i −0.717564 0.509389i
\(327\) −7.50434 + 4.33263i −0.414991 + 0.239595i
\(328\) −1.09009 + 0.601483i −0.0601902 + 0.0332113i
\(329\) 0 0
\(330\) −6.31820 0.593955i −0.347805 0.0326961i
\(331\) −3.00945 + 11.2314i −0.165414 + 0.617334i 0.832573 + 0.553915i \(0.186867\pi\)
−0.997987 + 0.0634183i \(0.979800\pi\)
\(332\) 8.65721 0.644733i 0.475126 0.0353843i
\(333\) 0.144474 + 0.539183i 0.00791711 + 0.0295470i
\(334\) −5.76797 + 15.5341i −0.315609 + 0.849990i
\(335\) −42.2509 −2.30841
\(336\) 0 0
\(337\) 15.7590 0.858445 0.429223 0.903199i \(-0.358788\pi\)
0.429223 + 0.903199i \(0.358788\pi\)
\(338\) 3.44976 9.29080i 0.187642 0.505353i
\(339\) 1.15963 + 4.32779i 0.0629823 + 0.235053i
\(340\) −1.17762 15.8126i −0.0638655 0.857560i
\(341\) −2.05928 + 7.68532i −0.111516 + 0.416183i
\(342\) 12.1988 + 1.14677i 0.659635 + 0.0620104i
\(343\) 0 0
\(344\) −6.15506 + 21.3090i −0.331859 + 1.14890i
\(345\) −4.49523 + 2.59533i −0.242015 + 0.139728i
\(346\) −12.6278 8.96428i −0.678873 0.481922i
\(347\) −14.7478 + 3.95167i −0.791706 + 0.212137i −0.631939 0.775018i \(-0.717741\pi\)
−0.159766 + 0.987155i \(0.551074\pi\)
\(348\) −0.145381 0.416095i −0.00779327 0.0223050i
\(349\) 6.62124 6.62124i 0.354427 0.354427i −0.507327 0.861754i \(-0.669366\pi\)
0.861754 + 0.507327i \(0.169366\pi\)
\(350\) 0 0
\(351\) 11.0467 0.589628
\(352\) −0.382357 6.95241i −0.0203797 0.370565i
\(353\) 10.9032 18.8849i 0.580319 1.00514i −0.415123 0.909765i \(-0.636261\pi\)
0.995441 0.0953759i \(-0.0304053\pi\)
\(354\) 0.343581 + 2.02502i 0.0182611 + 0.107628i
\(355\) −46.3931 12.4310i −2.46229 0.659769i
\(356\) −12.8441 2.43640i −0.680736 0.129129i
\(357\) 0 0
\(358\) 2.21257 23.5362i 0.116938 1.24393i
\(359\) −29.8216 + 17.2175i −1.57392 + 0.908704i −0.578241 + 0.815866i \(0.696261\pi\)
−0.995681 + 0.0928386i \(0.970406\pi\)
\(360\) −19.6436 + 18.8960i −1.03531 + 0.995908i
\(361\) −3.78856 2.18733i −0.199398 0.115123i
\(362\) −13.3186 29.0508i −0.700011 1.52687i
\(363\) −5.74807 5.74807i −0.301695 0.301695i
\(364\) 0 0
\(365\) −28.2399 + 28.2399i −1.47815 + 1.47815i
\(366\) 3.93822 10.6063i 0.205854 0.554400i
\(367\) 1.65812 2.87195i 0.0865533 0.149915i −0.819499 0.573081i \(-0.805748\pi\)
0.906052 + 0.423166i \(0.139081\pi\)
\(368\) −3.54677 4.45598i −0.184888 0.232284i
\(369\) −0.498611 0.863619i −0.0259566 0.0449582i
\(370\) −0.945402 1.14159i −0.0491491 0.0593487i
\(371\) 0 0
\(372\) −6.23727 9.15751i −0.323387 0.474795i
\(373\) 6.02667 22.4918i 0.312049 1.16458i −0.614656 0.788795i \(-0.710705\pi\)
0.926705 0.375789i \(-0.122628\pi\)
\(374\) −1.87807 + 2.64559i −0.0971124 + 0.136800i
\(375\) −25.5550 14.7542i −1.31966 0.761903i
\(376\) 10.5642 17.5046i 0.544805 0.902732i
\(377\) 0.629452i 0.0324184i
\(378\) 0 0
\(379\) 2.77271 + 2.77271i 0.142425 + 0.142425i 0.774724 0.632299i \(-0.217889\pi\)
−0.632299 + 0.774724i \(0.717889\pi\)
\(380\) −30.7143 + 10.7314i −1.57561 + 0.550511i
\(381\) −0.267209 0.997239i −0.0136895 0.0510901i
\(382\) −2.35603 13.8861i −0.120545 0.710473i
\(383\) 10.6953 + 18.5248i 0.546504 + 0.946572i 0.998511 + 0.0545578i \(0.0173749\pi\)
−0.452007 + 0.892014i \(0.649292\pi\)
\(384\) 7.68304 + 5.91523i 0.392073 + 0.301860i
\(385\) 0 0
\(386\) 8.76400 7.25783i 0.446076 0.369414i
\(387\) −17.1602 4.59806i −0.872302 0.233733i
\(388\) −2.58228 2.22431i −0.131095 0.112922i
\(389\) 24.3067 6.51295i 1.23240 0.330220i 0.416885 0.908959i \(-0.363122\pi\)
0.815512 + 0.578740i \(0.196455\pi\)
\(390\) −11.4724 + 5.25962i −0.580925 + 0.266331i
\(391\) 2.65372i 0.134204i
\(392\) 0 0
\(393\) 2.68058i 0.135217i
\(394\) −5.01727 10.9437i −0.252766 0.551337i
\(395\) 53.6564 14.3772i 2.69975 0.723395i
\(396\) 5.56167 0.414197i 0.279484 0.0208142i
\(397\) 0.377699 + 0.101204i 0.0189562 + 0.00507929i 0.268285 0.963340i \(-0.413543\pi\)
−0.249328 + 0.968419i \(0.580210\pi\)
\(398\) −13.3124 16.0750i −0.667288 0.805765i
\(399\) 0 0
\(400\) 19.1806 48.7384i 0.959028 2.43692i
\(401\) −9.92701 17.1941i −0.495731 0.858631i 0.504257 0.863554i \(-0.331766\pi\)
−0.999988 + 0.00492242i \(0.998433\pi\)
\(402\) −11.8692 + 2.01383i −0.591981 + 0.100440i
\(403\) 4.09534 + 15.2840i 0.204003 + 0.761350i
\(404\) 4.40493 + 2.12382i 0.219153 + 0.105664i
\(405\) −8.80940 8.80940i −0.437743 0.437743i
\(406\) 0 0
\(407\) 0.303284i 0.0150332i
\(408\) −1.08451 4.38598i −0.0536910 0.217138i
\(409\) 30.4501 + 17.5804i 1.50566 + 0.869295i 0.999978 + 0.00657643i \(0.00209336\pi\)
0.505685 + 0.862718i \(0.331240\pi\)
\(410\) 2.15924 + 1.53282i 0.106637 + 0.0757004i
\(411\) 0.0733461 0.273731i 0.00361789 0.0135022i
\(412\) 28.6630 + 5.43710i 1.41212 + 0.267866i
\(413\) 0 0
\(414\) 3.51333 2.90953i 0.172671 0.142996i
\(415\) −9.23185 15.9900i −0.453174 0.784920i
\(416\) −7.57175 11.5939i −0.371236 0.568435i
\(417\) −1.46230 + 2.53277i −0.0716089 + 0.124030i
\(418\) 6.24077 + 2.31725i 0.305246 + 0.113341i
\(419\) 17.1877 17.1877i 0.839673 0.839673i −0.149142 0.988816i \(-0.547651\pi\)
0.988816 + 0.149142i \(0.0476513\pi\)
\(420\) 0 0
\(421\) 12.9543 + 12.9543i 0.631352 + 0.631352i 0.948407 0.317055i \(-0.102694\pi\)
−0.317055 + 0.948407i \(0.602694\pi\)
\(422\) −26.3645 + 12.0871i −1.28340 + 0.588389i
\(423\) 14.1821 + 8.18803i 0.689557 + 0.398116i
\(424\) −19.6763 20.4548i −0.955566 0.993371i
\(425\) −21.1356 + 12.2026i −1.02523 + 0.591915i
\(426\) −13.6254 1.28088i −0.660150 0.0620588i
\(427\) 0 0
\(428\) 8.21868 5.59782i 0.397265 0.270581i
\(429\) 2.49433 + 0.668354i 0.120427 + 0.0322685i
\(430\) 46.5094 7.89117i 2.24288 0.380546i
\(431\) 2.85225 4.94025i 0.137388 0.237963i −0.789119 0.614240i \(-0.789463\pi\)
0.926507 + 0.376277i \(0.122796\pi\)
\(432\) −10.7325 + 14.5138i −0.516367 + 0.698297i
\(433\) 8.09187 0.388870 0.194435 0.980915i \(-0.437713\pi\)
0.194435 + 0.980915i \(0.437713\pi\)
\(434\) 0 0
\(435\) −0.662870 + 0.662870i −0.0317822 + 0.0317822i
\(436\) −8.78213 + 18.2147i −0.420588 + 0.872325i
\(437\) 5.25952 1.40928i 0.251597 0.0674152i
\(438\) −6.58719 + 9.27922i −0.314748 + 0.443378i
\(439\) 6.11379 3.52980i 0.291795 0.168468i −0.346956 0.937881i \(-0.612785\pi\)
0.638751 + 0.769413i \(0.279451\pi\)
\(440\) −12.9663 + 7.15446i −0.618145 + 0.341076i
\(441\) 0 0
\(442\) −0.603895 + 6.42394i −0.0287244 + 0.305556i
\(443\) 3.95466 14.7590i 0.187891 0.701221i −0.806102 0.591777i \(-0.798427\pi\)
0.993993 0.109443i \(-0.0349068\pi\)
\(444\) −0.319997 0.275638i −0.0151864 0.0130812i
\(445\) 7.19641 + 26.8574i 0.341142 + 1.27316i
\(446\) 6.26375 + 2.32579i 0.296597 + 0.110129i
\(447\) 2.09735 0.0992014
\(448\) 0 0
\(449\) 19.5020 0.920356 0.460178 0.887827i \(-0.347786\pi\)
0.460178 + 0.887827i \(0.347786\pi\)
\(450\) 39.3284 + 14.6030i 1.85396 + 0.688392i
\(451\) −0.140231 0.523350i −0.00660322 0.0246436i
\(452\) 7.92189 + 6.82374i 0.372615 + 0.320962i
\(453\) 2.92814 10.9280i 0.137576 0.513441i
\(454\) 2.17992 23.1889i 0.102309 1.08831i
\(455\) 0 0
\(456\) −8.11683 + 4.47865i −0.380105 + 0.209732i
\(457\) 8.72578 5.03783i 0.408175 0.235660i −0.281830 0.959464i \(-0.590942\pi\)
0.690005 + 0.723804i \(0.257608\pi\)
\(458\) 11.2791 15.8886i 0.527039 0.742427i
\(459\) 8.12437 2.17692i 0.379213 0.101610i
\(460\) −5.26066 + 10.9109i −0.245279 + 0.508725i
\(461\) 15.9419 15.9419i 0.742487 0.742487i −0.230569 0.973056i \(-0.574059\pi\)
0.973056 + 0.230569i \(0.0740587\pi\)
\(462\) 0 0
\(463\) −8.23452 −0.382690 −0.191345 0.981523i \(-0.561285\pi\)
−0.191345 + 0.981523i \(0.561285\pi\)
\(464\) −0.827013 0.611549i −0.0383931 0.0283904i
\(465\) −11.7827 + 20.4082i −0.546409 + 0.946408i
\(466\) 19.4496 3.29998i 0.900986 0.152869i
\(467\) 33.3801 + 8.94417i 1.54465 + 0.413887i 0.927764 0.373169i \(-0.121729\pi\)
0.616882 + 0.787055i \(0.288395\pi\)
\(468\) 9.16693 6.24368i 0.423741 0.288614i
\(469\) 0 0
\(470\) −43.2936 4.06991i −1.99699 0.187731i
\(471\) 2.65432 1.53247i 0.122305 0.0706126i
\(472\) 3.32288 + 3.45434i 0.152948 + 0.158999i
\(473\) −8.35922 4.82620i −0.384357 0.221909i
\(474\) 14.3880 6.59633i 0.660863 0.302979i
\(475\) 35.4092 + 35.4092i 1.62469 + 1.62469i
\(476\) 0 0
\(477\) 16.0749 16.0749i 0.736017 0.736017i
\(478\) 30.7305 + 11.4105i 1.40558 + 0.521905i
\(479\) −3.70229 + 6.41255i −0.169162 + 0.292997i −0.938125 0.346296i \(-0.887439\pi\)
0.768964 + 0.639293i \(0.220773\pi\)
\(480\) 4.23564 20.1831i 0.193330 0.921230i
\(481\) 0.301574 + 0.522342i 0.0137506 + 0.0238167i
\(482\) 4.56792 3.78288i 0.208063 0.172306i
\(483\) 0 0
\(484\) −18.6375 3.53536i −0.847160 0.160698i
\(485\) −1.87611 + 7.00175i −0.0851899 + 0.317933i
\(486\) −18.5068 13.1377i −0.839483 0.595938i
\(487\) 29.4458 + 17.0005i 1.33432 + 0.770368i 0.985958 0.166993i \(-0.0534056\pi\)
0.348359 + 0.937361i \(0.386739\pi\)
\(488\) −6.33747 25.6302i −0.286884 1.16022i
\(489\) 9.62880i 0.435429i
\(490\) 0 0
\(491\) 2.03871 + 2.03871i 0.0920055 + 0.0920055i 0.751612 0.659606i \(-0.229277\pi\)
−0.659606 + 0.751612i \(0.729277\pi\)
\(492\) 0.679638 + 0.327684i 0.0306404 + 0.0147732i
\(493\) 0.124043 + 0.462935i 0.00558662 + 0.0208496i
\(494\) 13.0526 2.21461i 0.587264 0.0996401i
\(495\) −5.93083 10.2725i −0.266571 0.461714i
\(496\) −24.0599 9.46858i −1.08032 0.425152i
\(497\) 0 0
\(498\) −3.35557 4.05193i −0.150367 0.181571i
\(499\) 13.8956 + 3.72332i 0.622053 + 0.166679i 0.556061 0.831141i \(-0.312312\pi\)
0.0659922 + 0.997820i \(0.478979\pi\)
\(500\) −68.6707 + 5.11415i −3.07105 + 0.228712i
\(501\) 9.69985 2.59907i 0.433357 0.116118i
\(502\) −13.8309 30.1681i −0.617303 1.34647i
\(503\) 27.2980i 1.21716i −0.793494 0.608579i \(-0.791740\pi\)
0.793494 0.608579i \(-0.208260\pi\)
\(504\) 0 0
\(505\) 10.4008i 0.462828i
\(506\) 2.25297 1.03290i 0.100157 0.0459178i
\(507\) −5.80138 + 1.55447i −0.257648 + 0.0690366i
\(508\) −1.82542 1.57237i −0.0809898 0.0697627i
\(509\) 19.9523 + 5.34620i 0.884370 + 0.236966i 0.672292 0.740286i \(-0.265310\pi\)
0.212078 + 0.977253i \(0.431977\pi\)
\(510\) −7.40095 + 6.12904i −0.327720 + 0.271398i
\(511\) 0 0
\(512\) 22.5891 + 1.31585i 0.998308 + 0.0581530i
\(513\) −8.62906 14.9460i −0.380982 0.659881i
\(514\) 2.61513 + 15.4132i 0.115349 + 0.679847i
\(515\) −16.0596 59.9351i −0.707669 2.64106i
\(516\) 12.6894 4.43361i 0.558619 0.195179i
\(517\) 6.29146 + 6.29146i 0.276698 + 0.276698i
\(518\) 0 0
\(519\) 9.38489i 0.411951i
\(520\) −15.2176 + 25.2153i −0.667335 + 1.10576i
\(521\) −9.46400 5.46404i −0.414625 0.239384i 0.278150 0.960538i \(-0.410279\pi\)
−0.692775 + 0.721154i \(0.743612\pi\)
\(522\) 0.476891 0.671785i 0.0208730 0.0294033i
\(523\) 3.18796 11.8976i 0.139400 0.520247i −0.860541 0.509381i \(-0.829875\pi\)
0.999941 0.0108660i \(-0.00345883\pi\)
\(524\) −3.52140 5.17009i −0.153833 0.225857i
\(525\) 0 0
\(526\) −14.7834 17.8513i −0.644588 0.778354i
\(527\) 6.02390 + 10.4337i 0.262405 + 0.454499i
\(528\) −3.30151 + 2.62787i −0.143680 + 0.114363i
\(529\) −10.4864 + 18.1630i −0.455930 + 0.789694i
\(530\) −21.0124 + 56.5901i −0.912722 + 2.45812i
\(531\) −2.71468 + 2.71468i −0.117807 + 0.117807i
\(532\) 0 0
\(533\) −0.761918 0.761918i −0.0330023 0.0330023i
\(534\) 3.30174 + 7.20181i 0.142880 + 0.311653i
\(535\) −18.3160 10.5747i −0.791868 0.457185i
\(536\) −20.2469 + 19.4763i −0.874532 + 0.841249i
\(537\) −12.4069 + 7.16316i −0.535399 + 0.309113i
\(538\) −0.170597 + 1.81472i −0.00735494 + 0.0782382i
\(539\) 0 0
\(540\) 37.7193 + 7.15499i 1.62318 + 0.307902i
\(541\) −16.2057 4.34231i −0.696739 0.186691i −0.106969 0.994262i \(-0.534115\pi\)
−0.589769 + 0.807572i \(0.700781\pi\)
\(542\) 4.76390 + 28.0777i 0.204627 + 1.20604i
\(543\) −9.68370 + 16.7727i −0.415567 + 0.719784i
\(544\) −7.85345 7.03466i −0.336714 0.301609i
\(545\) 43.0079 1.84226
\(546\) 0 0
\(547\) −23.2429 + 23.2429i −0.993797 + 0.993797i −0.999981 0.00618416i \(-0.998032\pi\)
0.00618416 + 0.999981i \(0.498032\pi\)
\(548\) −0.218129 0.624305i −0.00931800 0.0266690i
\(549\) 20.4266 5.47329i 0.871786 0.233594i
\(550\) 18.5864 + 13.1942i 0.792526 + 0.562603i
\(551\) 0.851637 0.491693i 0.0362810 0.0209468i
\(552\) −0.957780 + 3.31586i −0.0407658 + 0.141132i
\(553\) 0 0
\(554\) 45.4457 + 4.27222i 1.93080 + 0.181509i
\(555\) −0.232488 + 0.867659i −0.00986858 + 0.0368301i
\(556\) 0.506866 + 6.80599i 0.0214959 + 0.288638i
\(557\) 6.10578 + 22.7871i 0.258710 + 0.965519i 0.965989 + 0.258584i \(0.0832560\pi\)
−0.707279 + 0.706935i \(0.750077\pi\)
\(558\) 7.20884 19.4147i 0.305175 0.821888i
\(559\) −19.1960 −0.811904
\(560\) 0 0
\(561\) 1.96619 0.0830125
\(562\) −6.71783 + 18.0923i −0.283375 + 0.763177i
\(563\) −10.0847 37.6366i −0.425020 1.58620i −0.763880 0.645358i \(-0.776708\pi\)
0.338860 0.940837i \(-0.389959\pi\)
\(564\) −12.3561 + 0.920203i −0.520286 + 0.0387475i
\(565\) 5.75553 21.4799i 0.242137 0.903667i
\(566\) 26.4556 + 2.48701i 1.11201 + 0.104537i
\(567\) 0 0
\(568\) −27.9622 + 15.4288i −1.17327 + 0.647377i
\(569\) −10.2086 + 5.89395i −0.427968 + 0.247087i −0.698481 0.715629i \(-0.746140\pi\)
0.270513 + 0.962716i \(0.412807\pi\)
\(570\) 16.0778 + 11.4134i 0.673423 + 0.478054i
\(571\) 2.73214 0.732074i 0.114336 0.0306363i −0.201197 0.979551i \(-0.564483\pi\)
0.315534 + 0.948914i \(0.397817\pi\)
\(572\) 5.68888 1.98766i 0.237864 0.0831084i
\(573\) −6.03552 + 6.03552i −0.252138 + 0.252138i
\(574\) 0 0
\(575\) 18.6435 0.777489
\(576\) −0.702857 + 18.1102i −0.0292857 + 0.754591i
\(577\) −21.6020 + 37.4157i −0.899302 + 1.55764i −0.0709133 + 0.997482i \(0.522591\pi\)
−0.828389 + 0.560154i \(0.810742\pi\)
\(578\) −3.19983 18.8593i −0.133095 0.784445i
\(579\) −6.66100 1.78481i −0.276822 0.0741741i
\(580\) −0.407699 + 2.14929i −0.0169288 + 0.0892443i
\(581\) 0 0
\(582\) −0.193313 + 2.05637i −0.00801308 + 0.0852391i
\(583\) 10.6967 6.17574i 0.443012 0.255773i
\(584\) −0.515019 + 26.5505i −0.0213116 + 1.09867i
\(585\) −20.4292 11.7948i −0.844643 0.487655i
\(586\) 1.82897 + 3.98938i 0.0755542 + 0.164800i
\(587\) −28.1127 28.1127i −1.16034 1.16034i −0.984402 0.175935i \(-0.943705\pi\)
−0.175935 0.984402i \(-0.556295\pi\)
\(588\) 0 0
\(589\) 17.4799 17.4799i 0.720248 0.720248i
\(590\) 3.54852 9.55678i 0.146090 0.393446i
\(591\) −3.64795 + 6.31844i −0.150057 + 0.259906i
\(592\) −0.979282 0.111258i −0.0402483 0.00457268i
\(593\) −8.44544 14.6279i −0.346812 0.600697i 0.638869 0.769316i \(-0.279403\pi\)
−0.985681 + 0.168619i \(0.946069\pi\)
\(594\) −5.01038 6.05015i −0.205579 0.248241i
\(595\) 0 0
\(596\) 4.04521 2.75523i 0.165698 0.112859i
\(597\) −3.27371 + 12.2176i −0.133984 + 0.500035i
\(598\) 2.85318 4.01921i 0.116675 0.164358i
\(599\) −25.7194 14.8491i −1.05087 0.606718i −0.127975 0.991777i \(-0.540848\pi\)
−0.922892 + 0.385059i \(0.874181\pi\)
\(600\) −30.8134 + 7.61912i −1.25795 + 0.311049i
\(601\) 30.4663i 1.24275i 0.783515 + 0.621373i \(0.213425\pi\)
−0.783515 + 0.621373i \(0.786575\pi\)
\(602\) 0 0
\(603\) −15.9115 15.9115i −0.647966 0.647966i
\(604\) −8.70819 24.9236i −0.354331 1.01413i
\(605\) 10.4424 + 38.9715i 0.424544 + 1.58442i
\(606\) −0.495738 2.92180i −0.0201380 0.118690i
\(607\) 16.6272 + 28.7992i 0.674879 + 1.16892i 0.976504 + 0.215498i \(0.0691373\pi\)
−0.301626 + 0.953426i \(0.597529\pi\)
\(608\) −9.77165 + 19.3009i −0.396293 + 0.782756i
\(609\) 0 0
\(610\) −43.2486 + 35.8160i −1.75108 + 1.45015i
\(611\) 17.0917 + 4.57971i 0.691456 + 0.185275i
\(612\) 5.51148 6.39845i 0.222788 0.258642i
\(613\) 19.7780 5.29950i 0.798827 0.214045i 0.163758 0.986501i \(-0.447638\pi\)
0.635069 + 0.772456i \(0.280972\pi\)
\(614\) −15.0539 + 6.90162i −0.607526 + 0.278527i
\(615\) 1.60474i 0.0647093i
\(616\) 0 0
\(617\) 2.64884i 0.106638i 0.998578 + 0.0533192i \(0.0169801\pi\)
−0.998578 + 0.0533192i \(0.983020\pi\)
\(618\) −7.36820 16.0716i −0.296392 0.646495i
\(619\) −36.1940 + 9.69816i −1.45476 + 0.389802i −0.897677 0.440654i \(-0.854747\pi\)
−0.557084 + 0.830456i \(0.688080\pi\)
\(620\) 4.08415 + 54.8404i 0.164024 + 2.20244i
\(621\) −6.20631 1.66298i −0.249051 0.0667330i
\(622\) 7.67108 + 9.26300i 0.307582 + 0.371412i
\(623\) 0 0
\(624\) −3.07310 + 7.80884i −0.123023 + 0.312604i
\(625\) 40.4934 + 70.1366i 1.61974 + 2.80546i
\(626\) 22.7009 3.85163i 0.907311 0.153942i
\(627\) −1.04416 3.89687i −0.0416999 0.155626i
\(628\) 3.10628 6.44262i 0.123954 0.257089i
\(629\) 0.324731 + 0.324731i 0.0129479 + 0.0129479i
\(630\) 0 0
\(631\) 10.0919i 0.401753i −0.979617 0.200877i \(-0.935621\pi\)
0.979617 0.200877i \(-0.0643791\pi\)
\(632\) 19.0851 31.6236i 0.759163 1.25792i
\(633\) 15.2217 + 8.78826i 0.605009 + 0.349302i
\(634\) −26.0948 18.5243i −1.03636 0.735695i
\(635\) −1.32623 + 4.94955i −0.0526298 + 0.196417i
\(636\) −3.20556 + 16.8989i −0.127109 + 0.670086i
\(637\) 0 0
\(638\) 0.344744 0.285497i 0.0136486 0.0113029i
\(639\) −12.7900 22.1529i −0.505964 0.876355i
\(640\) −18.3446 44.4919i −0.725136 1.75870i
\(641\) −15.3814 + 26.6413i −0.607528 + 1.05227i 0.384118 + 0.923284i \(0.374505\pi\)
−0.991646 + 0.128986i \(0.958828\pi\)
\(642\) −5.64938 2.09767i −0.222963 0.0827883i
\(643\) −22.2297 + 22.2297i −0.876653 + 0.876653i −0.993187 0.116533i \(-0.962822\pi\)
0.116533 + 0.993187i \(0.462822\pi\)
\(644\) 0 0
\(645\) −20.2151 20.2151i −0.795970 0.795970i
\(646\) 9.16321 4.20097i 0.360522 0.165285i
\(647\) −14.3410 8.27978i −0.563803 0.325512i 0.190867 0.981616i \(-0.438870\pi\)
−0.754670 + 0.656104i \(0.772203\pi\)
\(648\) −8.28238 0.160659i −0.325363 0.00631129i
\(649\) −1.80643 + 1.04294i −0.0709085 + 0.0409390i
\(650\) 45.1309 + 4.24263i 1.77018 + 0.166409i
\(651\) 0 0
\(652\) 12.6491 + 18.5713i 0.495377 + 0.727308i
\(653\) 36.1075 + 9.67497i 1.41300 + 0.378611i 0.882993 0.469385i \(-0.155524\pi\)
0.530002 + 0.847996i \(0.322191\pi\)
\(654\) 12.0819 2.04991i 0.472438 0.0801578i
\(655\) −6.65220 + 11.5219i −0.259923 + 0.450200i
\(656\) 1.74130 0.260808i 0.0679865 0.0101829i
\(657\) −21.2701 −0.829824
\(658\) 0 0
\(659\) −14.8808 + 14.8808i −0.579674 + 0.579674i −0.934813 0.355139i \(-0.884433\pi\)
0.355139 + 0.934813i \(0.384433\pi\)
\(660\) 8.08410 + 3.89771i 0.314673 + 0.151718i
\(661\) −11.0651 + 2.96488i −0.430382 + 0.115321i −0.467506 0.883990i \(-0.654847\pi\)
0.0371232 + 0.999311i \(0.488181\pi\)
\(662\) 9.51873 13.4088i 0.369956 0.521148i
\(663\) 3.38634 1.95510i 0.131515 0.0759299i
\(664\) −11.7949 3.40693i −0.457730 0.132214i
\(665\) 0 0
\(666\) 0.0738851 0.785953i 0.00286299 0.0304551i
\(667\) 0.0947582 0.353642i 0.00366905 0.0136931i
\(668\) 15.2940 17.7553i 0.591743 0.686973i
\(669\) −1.04801 3.91122i −0.0405183 0.151217i
\(670\) 56.0150 + 20.7989i 2.16405 + 0.803530i
\(671\) 11.4897 0.443555
\(672\) 0 0
\(673\) 20.7704 0.800639 0.400319 0.916376i \(-0.368899\pi\)
0.400319 + 0.916376i \(0.368899\pi\)
\(674\) −20.8928 7.75768i −0.804759 0.298815i
\(675\) −15.2938 57.0772i −0.588658 2.19690i
\(676\) −9.14719 + 10.6193i −0.351815 + 0.408433i
\(677\) 7.11687 26.5605i 0.273524 1.02080i −0.683301 0.730137i \(-0.739456\pi\)
0.956824 0.290667i \(-0.0938772\pi\)
\(678\) 0.593044 6.30851i 0.0227757 0.242277i
\(679\) 0 0
\(680\) −6.22284 + 21.5436i −0.238635 + 0.826161i
\(681\) −12.2239 + 7.05746i −0.468420 + 0.270442i
\(682\) 6.51339 9.17525i 0.249410 0.351339i
\(683\) 2.08533 0.558762i 0.0797928 0.0213804i −0.218702 0.975792i \(-0.570182\pi\)
0.298495 + 0.954411i \(0.403516\pi\)
\(684\) −15.6083 7.52547i −0.596798 0.287744i
\(685\) −0.994563 + 0.994563i −0.0380003 + 0.0380003i
\(686\) 0 0
\(687\) −11.8083 −0.450517
\(688\) 18.6500 25.2209i 0.711025 0.961537i
\(689\) 12.2819 21.2728i 0.467902 0.810429i
\(690\) 7.23726 1.22793i 0.275518 0.0467466i
\(691\) −2.35594 0.631272i −0.0896242 0.0240147i 0.213728 0.976893i \(-0.431439\pi\)
−0.303352 + 0.952878i \(0.598106\pi\)
\(692\) 12.3287 + 18.1009i 0.468666 + 0.688091i
\(693\) 0 0
\(694\) 21.4976 + 2.02092i 0.816036 + 0.0767131i
\(695\) 12.5708 7.25775i 0.476837 0.275302i
\(696\) −0.0120889 + 0.623214i −0.000458230 + 0.0236229i
\(697\) −0.710506 0.410211i −0.0269124 0.0155379i
\(698\) −12.0377 + 5.51880i −0.455633 + 0.208890i
\(699\) −8.45369 8.45369i −0.319748 0.319748i
\(700\) 0 0
\(701\) 6.81795 6.81795i 0.257510 0.257510i −0.566530 0.824041i \(-0.691715\pi\)
0.824041 + 0.566530i \(0.191715\pi\)
\(702\) −14.6454 5.43796i −0.552754 0.205243i
\(703\) 0.471146 0.816049i 0.0177696 0.0307779i
\(704\) −2.91555 + 9.40553i −0.109884 + 0.354484i
\(705\) 13.1763 + 22.8220i 0.496247 + 0.859525i
\(706\) −23.7516 + 19.6697i −0.893904 + 0.740280i
\(707\) 0 0
\(708\) 0.541347 2.85384i 0.0203450 0.107254i
\(709\) −3.04470 + 11.3630i −0.114346 + 0.426745i −0.999237 0.0390527i \(-0.987566\pi\)
0.884891 + 0.465798i \(0.154233\pi\)
\(710\) 55.3873 + 39.3187i 2.07865 + 1.47560i
\(711\) 25.6212 + 14.7924i 0.960869 + 0.554758i
\(712\) 15.8290 + 9.55289i 0.593216 + 0.358010i
\(713\) 9.20346i 0.344672i
\(714\) 0 0
\(715\) −9.06280 9.06280i −0.338929 0.338929i
\(716\) −14.5195 + 30.1144i −0.542621 + 1.12543i
\(717\) −5.14163 19.1888i −0.192018 0.716619i
\(718\) 48.0123 8.14616i 1.79180 0.304012i
\(719\) 16.4827 + 28.5490i 0.614703 + 1.06470i 0.990437 + 0.137969i \(0.0440573\pi\)
−0.375734 + 0.926728i \(0.622609\pi\)
\(720\) 35.3449 15.3818i 1.31723 0.573247i
\(721\) 0 0
\(722\) 3.94601 + 4.76490i 0.146855 + 0.177331i
\(723\) −3.47180 0.930267i −0.129118 0.0345970i
\(724\) 3.35660 + 45.0710i 0.124747 + 1.67505i
\(725\) 3.25232 0.871457i 0.120788 0.0323651i
\(726\) 4.79102 + 10.4502i 0.177811 + 0.387844i
\(727\) 13.8871i 0.515045i 0.966272 + 0.257523i \(0.0829062\pi\)
−0.966272 + 0.257523i \(0.917094\pi\)
\(728\) 0 0
\(729\) 4.96768i 0.183988i
\(730\) 51.3414 23.5380i 1.90023 0.871180i
\(731\) −14.1178 + 3.78286i −0.522167 + 0.139914i
\(732\) −10.4424 + 12.1229i −0.385960 + 0.448074i
\(733\) −10.6925 2.86505i −0.394936 0.105823i 0.0558846 0.998437i \(-0.482202\pi\)
−0.450821 + 0.892614i \(0.648869\pi\)
\(734\) −3.61207 + 2.99131i −0.133324 + 0.110411i
\(735\) 0 0
\(736\) 2.50866 + 7.65359i 0.0924704 + 0.282115i
\(737\) −6.11297 10.5880i −0.225174 0.390013i
\(738\) 0.235909 + 1.39041i 0.00868393 + 0.0511818i
\(739\) −2.88999 10.7856i −0.106310 0.396754i 0.892181 0.451679i \(-0.149175\pi\)
−0.998490 + 0.0549249i \(0.982508\pi\)
\(740\) 0.691413 + 1.97889i 0.0254169 + 0.0727453i
\(741\) −5.67325 5.67325i −0.208412 0.208412i
\(742\) 0 0
\(743\) 49.5292i 1.81705i −0.417832 0.908524i \(-0.637210\pi\)
0.417832 0.908524i \(-0.362790\pi\)
\(744\) 3.76121 + 15.2112i 0.137893 + 0.557669i
\(745\) −9.01507 5.20485i −0.330287 0.190691i
\(746\) −19.0621 + 26.8523i −0.697912 + 0.983132i
\(747\) 2.54510 9.49845i 0.0931204 0.347530i
\(748\) 3.79223 2.58292i 0.138658 0.0944411i
\(749\) 0 0
\(750\) 26.6170 + 32.1407i 0.971917 + 1.17361i
\(751\) 0.523146 + 0.906116i 0.0190899 + 0.0330646i 0.875413 0.483377i \(-0.160590\pi\)
−0.856323 + 0.516441i \(0.827256\pi\)
\(752\) −22.6227 + 18.0067i −0.824964 + 0.656637i
\(753\) −10.0562 + 17.4178i −0.366467 + 0.634739i
\(754\) 0.309861 0.834509i 0.0112845 0.0303910i
\(755\) −39.7052 + 39.7052i −1.44502 + 1.44502i
\(756\) 0 0
\(757\) −29.5274 29.5274i −1.07319 1.07319i −0.997101 0.0760892i \(-0.975757\pi\)
−0.0760892 0.997101i \(-0.524243\pi\)
\(758\) −2.31106 5.04091i −0.0839414 0.183094i
\(759\) −1.30077 0.750998i −0.0472148 0.0272595i
\(760\) 46.0030 + 0.892353i 1.66870 + 0.0323690i
\(761\) 33.9144 19.5805i 1.22940 0.709793i 0.262493 0.964934i \(-0.415455\pi\)
0.966904 + 0.255141i \(0.0821220\pi\)
\(762\) −0.136653 + 1.45365i −0.00495043 + 0.0526602i
\(763\) 0 0
\(764\) −3.71216 + 19.5696i −0.134301 + 0.708002i
\(765\) −17.3492 4.64869i −0.627260 0.168074i
\(766\) −5.06029 29.8246i −0.182836 1.07761i
\(767\) −2.07412 + 3.59249i −0.0748923 + 0.129717i
\(768\) −7.27405 11.6244i −0.262480 0.419459i
\(769\) −28.7025 −1.03504 −0.517519 0.855672i \(-0.673144\pi\)
−0.517519 + 0.855672i \(0.673144\pi\)
\(770\) 0 0
\(771\) 6.69929 6.69929i 0.241269 0.241269i
\(772\) −15.1919 + 5.30796i −0.546768 + 0.191038i
\(773\) 14.5617 3.90180i 0.523748 0.140338i 0.0127485 0.999919i \(-0.495942\pi\)
0.511000 + 0.859581i \(0.329275\pi\)
\(774\) 20.4870 + 14.5434i 0.736390 + 0.522753i
\(775\) 73.3012 42.3205i 2.63306 1.52020i
\(776\) 2.32854 + 4.22011i 0.0835899 + 0.151493i
\(777\) 0 0
\(778\) −35.4312 3.33078i −1.27027 0.119414i
\(779\) −0.435693 + 1.62603i −0.0156103 + 0.0582586i
\(780\) 17.7989 1.32555i 0.637302 0.0474621i
\(781\) −3.59710 13.4246i −0.128715 0.480369i
\(782\) 1.30635 3.51823i 0.0467150 0.125811i
\(783\) −1.16041 −0.0414697
\(784\) 0 0
\(785\) −15.2121 −0.542944
\(786\) −1.31957 + 3.55383i −0.0470675 + 0.126761i
\(787\) 6.06728 + 22.6434i 0.216275 + 0.807150i 0.985714 + 0.168429i \(0.0538695\pi\)
−0.769438 + 0.638721i \(0.779464\pi\)
\(788\) 1.26447 + 16.9787i 0.0450447 + 0.604842i
\(789\) −3.63546 + 13.5677i −0.129426 + 0.483024i
\(790\) −78.2136 7.35263i −2.78272 0.261595i
\(791\) 0 0
\(792\) −7.57739 2.18872i −0.269251 0.0777727i
\(793\) 19.7886 11.4249i 0.702713 0.405712i
\(794\) −0.450923 0.320104i −0.0160027 0.0113601i
\(795\) 35.3361 9.46828i 1.25324 0.335805i
\(796\) 9.73590 + 27.8650i 0.345080 + 0.987649i
\(797\) −3.81531 + 3.81531i −0.135145 + 0.135145i −0.771443 0.636298i \(-0.780465\pi\)
0.636298 + 0.771443i \(0.280465\pi\)
\(798\) 0 0
\(799\) 13.4727 0.476631
\(800\) −49.4215 + 55.1739i −1.74732 + 1.95069i
\(801\) −7.40422 + 12.8245i −0.261615 + 0.453131i
\(802\) 4.69679 + 27.6822i 0.165850 + 0.977492i
\(803\) −11.1627 2.99104i −0.393923 0.105551i
\(804\) 16.7272 + 3.17298i 0.589922 + 0.111903i
\(805\) 0 0
\(806\) 2.09439 22.2791i 0.0737718 0.784748i
\(807\) 0.956619 0.552304i 0.0336746 0.0194420i
\(808\) −4.79443 4.98411i −0.168668 0.175341i
\(809\) 24.7881 + 14.3114i 0.871505 + 0.503164i 0.867848 0.496830i \(-0.165503\pi\)
0.00365682 + 0.999993i \(0.498836\pi\)
\(810\) 7.34264 + 16.0159i 0.257994 + 0.562740i
\(811\) −9.30808 9.30808i −0.326851 0.326851i 0.524537 0.851388i \(-0.324238\pi\)
−0.851388 + 0.524537i \(0.824238\pi\)
\(812\) 0 0
\(813\) 12.2039 12.2039i 0.428008 0.428008i
\(814\) 0.149298 0.402085i 0.00523288 0.0140931i
\(815\) 23.8951 41.3875i 0.837009 1.44974i
\(816\) −0.721286 + 6.34868i −0.0252500 + 0.222248i
\(817\) 14.9948 + 25.9718i 0.524603 + 0.908639i
\(818\) −31.7156 38.2973i −1.10891 1.33903i
\(819\) 0 0
\(820\) −2.10810 3.09510i −0.0736180 0.108085i
\(821\) 4.31850 16.1169i 0.150717 0.562482i −0.848718 0.528846i \(-0.822625\pi\)
0.999434 0.0336357i \(-0.0107086\pi\)
\(822\) −0.231990 + 0.326799i −0.00809158 + 0.0113984i
\(823\) −9.41497 5.43573i −0.328185 0.189478i 0.326850 0.945076i \(-0.394013\pi\)
−0.655035 + 0.755598i \(0.727346\pi\)
\(824\) −35.3241 21.3183i −1.23057 0.742658i
\(825\) 13.8133i 0.480918i
\(826\) 0 0
\(827\) 9.97483 + 9.97483i 0.346859 + 0.346859i 0.858938 0.512079i \(-0.171125\pi\)
−0.512079 + 0.858938i \(0.671125\pi\)
\(828\) −6.09015 + 2.12787i −0.211647 + 0.0739485i
\(829\) 6.68921 + 24.9645i 0.232326 + 0.867052i 0.979336 + 0.202240i \(0.0648220\pi\)
−0.747010 + 0.664813i \(0.768511\pi\)
\(830\) 4.36789 + 25.7437i 0.151612 + 0.893577i
\(831\) −13.8312 23.9564i −0.479801 0.831039i
\(832\) 4.33109 + 19.0982i 0.150154 + 0.662109i
\(833\) 0 0
\(834\) 3.18548 2.63803i 0.110304 0.0913475i
\(835\) −48.1428 12.8998i −1.66605 0.446417i
\(836\) −7.13311 6.14430i −0.246704 0.212505i
\(837\) −28.1764 + 7.54985i −0.973920 + 0.260961i
\(838\) −31.2479 + 14.3259i −1.07944 + 0.494881i
\(839\) 35.9931i 1.24262i 0.783565 + 0.621310i \(0.213399\pi\)
−0.783565 + 0.621310i \(0.786601\pi\)
\(840\) 0 0
\(841\) 28.9339i 0.997720i
\(842\) −10.7974 23.5514i −0.372102 0.811634i
\(843\) 11.2972 3.02708i 0.389097 0.104258i
\(844\) 40.9034 3.04622i 1.40795 0.104855i
\(845\) 28.7937 + 7.71526i 0.990535 + 0.265413i
\(846\) −14.7715 17.8369i −0.507854 0.613245i
\(847\) 0 0
\(848\) 16.0170 + 36.8044i 0.550026 + 1.26387i
\(849\) −8.05167 13.9459i −0.276333 0.478622i
\(850\) 34.0280 5.77347i 1.16715 0.198029i
\(851\) −0.0907985 0.338864i −0.00311253 0.0116161i
\(852\) 17.4336 + 8.40552i 0.597264 + 0.287968i
\(853\) −11.5045 11.5045i −0.393906 0.393906i 0.482171 0.876077i \(-0.339848\pi\)
−0.876077 + 0.482171i \(0.839848\pi\)
\(854\) 0 0
\(855\) 36.8538i 1.26037i
\(856\) −13.6517 + 3.37561i −0.466607 + 0.115376i
\(857\) −46.8795 27.0659i −1.60137 0.924554i −0.991213 0.132276i \(-0.957771\pi\)
−0.610161 0.792277i \(-0.708895\pi\)
\(858\) −2.97790 2.11397i −0.101664 0.0721698i
\(859\) −1.84230 + 6.87557i −0.0628586 + 0.234591i −0.990207 0.139608i \(-0.955416\pi\)
0.927348 + 0.374199i \(0.122082\pi\)
\(860\) −65.5454 12.4333i −2.23508 0.423973i
\(861\) 0 0
\(862\) −6.21337 + 5.14555i −0.211628 + 0.175258i
\(863\) −8.29596 14.3690i −0.282398 0.489127i 0.689577 0.724212i \(-0.257796\pi\)
−0.971975 + 0.235085i \(0.924463\pi\)
\(864\) 21.3736 13.9587i 0.727143 0.474885i
\(865\) 23.2898 40.3391i 0.791877 1.37157i
\(866\) −10.7280 3.98339i −0.364551 0.135361i
\(867\) −8.19713 + 8.19713i −0.278389 + 0.278389i
\(868\) 0 0
\(869\) 11.3661 + 11.3661i 0.385567 + 0.385567i
\(870\) 1.20513 0.552502i 0.0408576 0.0187316i
\(871\) −21.0566 12.1570i −0.713475 0.411925i
\(872\) 20.6097 19.8253i 0.697931 0.671370i
\(873\) −3.34336 + 1.93029i −0.113156 + 0.0653305i
\(874\) −7.66667 0.720721i −0.259329 0.0243788i
\(875\) 0 0
\(876\) 13.3010 9.05944i 0.449399 0.306090i
\(877\) 29.3202 + 7.85634i 0.990074 + 0.265290i 0.717282 0.696783i \(-0.245386\pi\)
0.272793 + 0.962073i \(0.412053\pi\)
\(878\) −9.84311 + 1.67006i −0.332189 + 0.0563619i
\(879\) 1.32981 2.30330i 0.0448534 0.0776883i
\(880\) 20.7123 3.10224i 0.698212 0.104577i
\(881\) 48.7213 1.64146 0.820731 0.571314i \(-0.193566\pi\)
0.820731 + 0.571314i \(0.193566\pi\)
\(882\) 0 0
\(883\) 2.32744 2.32744i 0.0783247 0.0783247i −0.666859 0.745184i \(-0.732362\pi\)
0.745184 + 0.666859i \(0.232362\pi\)
\(884\) 3.96295 8.21939i 0.133288 0.276448i
\(885\) −5.96746 + 1.59898i −0.200594 + 0.0537490i
\(886\) −12.5084 + 17.6203i −0.420228 + 0.591965i
\(887\) −45.9577 + 26.5337i −1.54311 + 0.890914i −0.544467 + 0.838782i \(0.683268\pi\)
−0.998640 + 0.0521315i \(0.983399\pi\)
\(888\) 0.288554 + 0.522957i 0.00968323 + 0.0175493i
\(889\) 0 0
\(890\) 3.68031 39.1493i 0.123364 1.31229i
\(891\) 0.933049 3.48219i 0.0312583 0.116658i
\(892\) −7.15938 6.16692i −0.239714 0.206484i
\(893\) −7.15483 26.7022i −0.239427 0.893555i
\(894\) −2.78061 1.03247i −0.0929975 0.0345308i
\(895\) 71.1052 2.37678
\(896\) 0 0
\(897\) −2.98706 −0.0997350
\(898\) −25.8552 9.60026i −0.862798 0.320365i
\(899\) −0.430199 1.60552i −0.0143479 0.0535472i
\(900\) −44.9519 38.7205i −1.49840 1.29068i
\(901\) 4.84066 18.0656i 0.161266 0.601852i
\(902\) −0.0717155 + 0.762874i −0.00238786 + 0.0254009i
\(903\) 0 0
\(904\) −7.14349 12.9464i −0.237589 0.430592i
\(905\) 83.2470 48.0627i 2.76723 1.59766i
\(906\) −9.26156 + 13.0465i −0.307695 + 0.433442i
\(907\) −53.9154 + 14.4466i −1.79023 + 0.479691i −0.992385 0.123172i \(-0.960693\pi\)
−0.797845 + 0.602863i \(0.794027\pi\)
\(908\) −14.3053 + 29.6701i −0.474738 + 0.984635i
\(909\) 3.91688 3.91688i 0.129915 0.129915i
\(910\) 0 0
\(911\) −44.7554 −1.48281 −0.741406 0.671057i \(-0.765841\pi\)
−0.741406 + 0.671057i \(0.765841\pi\)
\(912\) 12.9658 1.94198i 0.429340 0.0643055i
\(913\) 2.67138 4.62696i 0.0884097 0.153130i
\(914\) −14.0484 + 2.38356i −0.464678 + 0.0788412i
\(915\) 32.8707 + 8.80768i 1.08667 + 0.291173i
\(916\) −22.7750 + 15.5123i −0.752509 + 0.512541i
\(917\) 0 0
\(918\) −11.8427 1.11330i −0.390867 0.0367443i
\(919\) −19.8098 + 11.4372i −0.653464 + 0.377277i −0.789782 0.613388i \(-0.789806\pi\)
0.136318 + 0.990665i \(0.456473\pi\)
\(920\) 12.3456 11.8757i 0.407021 0.391531i
\(921\) 8.69148 + 5.01803i 0.286394 + 0.165350i
\(922\) −28.9830 + 13.2876i −0.954504 + 0.437602i
\(923\) −19.5442 19.5442i −0.643304 0.643304i
\(924\) 0 0
\(925\) 2.28137 2.28137i 0.0750111 0.0750111i
\(926\) 10.9171 + 4.05361i 0.358758 + 0.133210i
\(927\) 16.5233 28.6192i 0.542697 0.939979i
\(928\) 0.795383 + 1.21789i 0.0261097 + 0.0399791i
\(929\) −13.2871 23.0139i −0.435935 0.755062i 0.561436 0.827520i \(-0.310249\pi\)
−0.997371 + 0.0724577i \(0.976916\pi\)
\(930\) 25.6675 21.2563i 0.841671 0.697023i
\(931\) 0 0
\(932\) −27.4102 5.19946i −0.897852 0.170314i
\(933\) 1.88643 7.04026i 0.0617590 0.230488i
\(934\) −39.8514 28.2900i −1.30398 0.925676i
\(935\) −8.45127 4.87934i −0.276386 0.159572i
\(936\) −15.2268 + 3.76508i −0.497705 + 0.123066i
\(937\) 11.8582i 0.387391i 0.981062 + 0.193696i \(0.0620474\pi\)
−0.981062 + 0.193696i \(0.937953\pi\)
\(938\) 0 0
\(939\) −9.86686 9.86686i −0.321993 0.321993i
\(940\) 55.3939 + 26.7080i 1.80675 + 0.871118i
\(941\) −0.548049 2.04535i −0.0178659 0.0666764i 0.956417 0.292003i \(-0.0943217\pi\)
−0.974283 + 0.225327i \(0.927655\pi\)
\(942\) −4.27341 + 0.725063i −0.139235 + 0.0236238i
\(943\) 0.313366 + 0.542765i 0.0102046 + 0.0176749i
\(944\) −2.70491 6.21542i −0.0880372 0.202295i
\(945\) 0 0
\(946\) 8.70662 + 10.5134i 0.283077 + 0.341821i
\(947\) −5.18291 1.38876i −0.168422 0.0451285i 0.173623 0.984812i \(-0.444453\pi\)
−0.342045 + 0.939684i \(0.611119\pi\)
\(948\) −22.3224 + 1.66243i −0.724997 + 0.0539931i
\(949\) −22.1995 + 5.94835i −0.720628 + 0.193092i
\(950\) −29.5136 64.3755i −0.957548 2.08862i
\(951\) 19.3935i 0.628878i
\(952\) 0 0
\(953\) 3.43130i 0.111151i 0.998454 + 0.0555753i \(0.0176993\pi\)
−0.998454 + 0.0555753i \(0.982301\pi\)
\(954\) −29.2248 + 13.3984i −0.946187 + 0.433789i
\(955\) 40.9205 10.9646i 1.32415 0.354806i
\(956\) −35.1246 30.2555i −1.13601 0.978533i
\(957\) −0.262020 0.0702080i −0.00846989 0.00226950i
\(958\) 8.06510 6.67905i 0.260572 0.215790i
\(959\) 0 0
\(960\) −15.5511 + 24.6731i −0.501908 + 0.796322i
\(961\) −5.39169 9.33869i −0.173926 0.301248i
\(962\) −0.142685 0.840962i −0.00460034 0.0271137i
\(963\) −2.91531 10.8801i −0.0939446 0.350606i
\(964\) −7.91822 + 2.76658i −0.255029 + 0.0891057i
\(965\) 24.2018 + 24.2018i 0.779083 + 0.779083i
\(966\) 0 0
\(967\) 19.4110i 0.624217i 0.950046 + 0.312108i \(0.101035\pi\)
−0.950046 + 0.312108i \(0.898965\pi\)
\(968\) 22.9687 + 13.8618i 0.738243 + 0.445535i
\(969\) −5.29044 3.05444i −0.169954 0.0981227i
\(970\) 5.93406 8.35916i 0.190531 0.268397i
\(971\) 5.21341 19.4567i 0.167306 0.624396i −0.830428 0.557125i \(-0.811904\pi\)
0.997735 0.0672705i \(-0.0214291\pi\)
\(972\) 18.0684 + 26.5279i 0.579545 + 0.850883i
\(973\) 0 0
\(974\) −30.6695 37.0342i −0.982715 1.18665i
\(975\) −13.7354 23.7905i −0.439886 0.761905i
\(976\) −4.21494 + 37.0995i −0.134917 + 1.18753i
\(977\) −8.78731 + 15.2201i −0.281131 + 0.486933i −0.971664 0.236368i \(-0.924043\pi\)
0.690533 + 0.723301i \(0.257376\pi\)
\(978\) 4.73998 12.7656i 0.151568 0.408199i
\(979\) −5.68920 + 5.68920i −0.181828 + 0.181828i
\(980\) 0 0
\(981\) 16.1966 + 16.1966i 0.517117 + 0.517117i
\(982\) −1.69926 3.70645i −0.0542256 0.118278i
\(983\) 47.7497 + 27.5683i 1.52298 + 0.879292i 0.999631 + 0.0271723i \(0.00865028\pi\)
0.523347 + 0.852119i \(0.324683\pi\)
\(984\) −0.739734 0.769000i −0.0235819 0.0245148i
\(985\) 31.3600 18.1057i 0.999214 0.576896i
\(986\) 0.0634368 0.674809i 0.00202024 0.0214903i
\(987\) 0 0
\(988\) −18.3949 3.48934i −0.585221 0.111011i
\(989\) 10.7848 + 2.88978i 0.342937 + 0.0918896i
\(990\) 2.80607 + 16.5386i 0.0891828 + 0.525630i
\(991\) 18.4719 31.9943i 0.586781 1.01633i −0.407870 0.913040i \(-0.633728\pi\)
0.994651 0.103294i \(-0.0329382\pi\)
\(992\) 27.2369 + 24.3972i 0.864771 + 0.774611i
\(993\) −9.96536 −0.316241
\(994\) 0 0
\(995\) 44.3910 44.3910i 1.40729 1.40729i
\(996\) 2.45407 + 7.02378i 0.0777602 + 0.222557i
\(997\) −3.58236 + 0.959891i −0.113455 + 0.0304001i −0.315100 0.949059i \(-0.602038\pi\)
0.201645 + 0.979459i \(0.435371\pi\)
\(998\) −16.5895 11.7767i −0.525132 0.372784i
\(999\) −0.962950 + 0.555960i −0.0304664 + 0.0175898i
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.o.165.2 48
7.2 even 3 inner 784.2.x.o.373.7 48
7.3 odd 6 784.2.m.j.197.9 24
7.4 even 3 784.2.m.k.197.9 24
7.5 odd 6 112.2.w.c.37.7 48
7.6 odd 2 112.2.w.c.53.2 yes 48
16.13 even 4 inner 784.2.x.o.557.7 48
28.19 even 6 448.2.ba.c.177.6 48
28.27 even 2 448.2.ba.c.305.7 48
56.5 odd 6 896.2.ba.f.737.6 48
56.13 odd 2 896.2.ba.f.865.7 48
56.19 even 6 896.2.ba.e.737.7 48
56.27 even 2 896.2.ba.e.865.6 48
112.5 odd 12 896.2.ba.f.289.7 48
112.13 odd 4 112.2.w.c.109.7 yes 48
112.19 even 12 448.2.ba.c.401.7 48
112.27 even 4 896.2.ba.e.417.7 48
112.45 odd 12 784.2.m.j.589.9 24
112.61 odd 12 112.2.w.c.93.2 yes 48
112.69 odd 4 896.2.ba.f.417.6 48
112.75 even 12 896.2.ba.e.289.6 48
112.83 even 4 448.2.ba.c.81.6 48
112.93 even 12 inner 784.2.x.o.765.2 48
112.109 even 12 784.2.m.k.589.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.7 48 7.5 odd 6
112.2.w.c.53.2 yes 48 7.6 odd 2
112.2.w.c.93.2 yes 48 112.61 odd 12
112.2.w.c.109.7 yes 48 112.13 odd 4
448.2.ba.c.81.6 48 112.83 even 4
448.2.ba.c.177.6 48 28.19 even 6
448.2.ba.c.305.7 48 28.27 even 2
448.2.ba.c.401.7 48 112.19 even 12
784.2.m.j.197.9 24 7.3 odd 6
784.2.m.j.589.9 24 112.45 odd 12
784.2.m.k.197.9 24 7.4 even 3
784.2.m.k.589.9 24 112.109 even 12
784.2.x.o.165.2 48 1.1 even 1 trivial
784.2.x.o.373.7 48 7.2 even 3 inner
784.2.x.o.557.7 48 16.13 even 4 inner
784.2.x.o.765.2 48 112.93 even 12 inner
896.2.ba.e.289.6 48 112.75 even 12
896.2.ba.e.417.7 48 112.27 even 4
896.2.ba.e.737.7 48 56.19 even 6
896.2.ba.e.865.6 48 56.27 even 2
896.2.ba.f.289.7 48 112.5 odd 12
896.2.ba.f.417.6 48 112.69 odd 4
896.2.ba.f.737.6 48 56.5 odd 6
896.2.ba.f.865.7 48 56.13 odd 2