Properties

Label 175.2.t.a.109.13
Level $175$
Weight $2$
Character 175.109
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(4,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([3, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.t (of order \(30\), degree \(8\), 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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 109.13
Character \(\chi\) \(=\) 175.109
Dual form 175.2.t.a.114.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.46946 + 0.154447i) q^{2} +(0.0450101 - 0.211756i) q^{3} +(0.179176 + 0.0380851i) q^{4} +(0.796997 - 2.08921i) q^{5} +(0.0988458 - 0.304216i) q^{6} +(2.55064 - 0.703027i) q^{7} +(-2.55307 - 0.829544i) q^{8} +(2.69782 + 1.20115i) q^{9} +O(q^{10})\) \(q+(1.46946 + 0.154447i) q^{2} +(0.0450101 - 0.211756i) q^{3} +(0.179176 + 0.0380851i) q^{4} +(0.796997 - 2.08921i) q^{5} +(0.0988458 - 0.304216i) q^{6} +(2.55064 - 0.703027i) q^{7} +(-2.55307 - 0.829544i) q^{8} +(2.69782 + 1.20115i) q^{9} +(1.49383 - 2.94692i) q^{10} +(-5.12740 + 2.28287i) q^{11} +(0.0161295 - 0.0362274i) q^{12} +(2.43682 + 3.35400i) q^{13} +(3.85665 - 0.639135i) q^{14} +(-0.406529 - 0.262804i) q^{15} +(-3.95821 - 1.76231i) q^{16} +(-1.54544 + 1.39152i) q^{17} +(3.77884 + 2.18171i) q^{18} +(1.18938 - 0.252810i) q^{19} +(0.222371 - 0.343983i) q^{20} +(-0.0340657 - 0.571756i) q^{21} +(-7.88712 + 2.56268i) q^{22} +(-5.39196 - 0.566717i) q^{23} +(-0.290575 + 0.503290i) q^{24} +(-3.72959 - 3.33019i) q^{25} +(3.06281 + 5.30495i) q^{26} +(0.757522 - 1.04264i) q^{27} +(0.483788 - 0.0288245i) q^{28} +(0.466053 + 1.43436i) q^{29} +(-0.556791 - 0.448969i) q^{30} +(-1.46756 - 1.62989i) q^{31} +(-0.894649 - 0.516526i) q^{32} +(0.252626 + 1.18851i) q^{33} +(-2.48589 + 1.80610i) q^{34} +(0.564081 - 5.88913i) q^{35} +(0.437639 + 0.317964i) q^{36} +(-0.927175 + 2.08247i) q^{37} +(1.78679 - 0.187800i) q^{38} +(0.819911 - 0.365048i) q^{39} +(-3.76788 + 4.67276i) q^{40} +(0.645691 - 0.469122i) q^{41} +(0.0382477 - 0.845436i) q^{42} -4.15020i q^{43} +(-1.00565 + 0.213758i) q^{44} +(4.65961 - 4.67900i) q^{45} +(-7.83576 - 1.66554i) q^{46} +(9.01773 + 8.11960i) q^{47} +(-0.551339 + 0.758853i) q^{48} +(6.01151 - 3.58633i) q^{49} +(-4.96616 - 5.46962i) q^{50} +(0.225102 + 0.389889i) q^{51} +(0.308883 + 0.693764i) q^{52} +(-2.22754 + 10.4798i) q^{53} +(1.27418 - 1.41513i) q^{54} +(0.682859 + 12.5317i) q^{55} +(-7.09515 - 0.320986i) q^{56} -0.263237i q^{57} +(0.463315 + 2.17973i) q^{58} +(-1.05882 - 10.0740i) q^{59} +(-0.0628314 - 0.0625710i) q^{60} +(0.761635 - 7.24647i) q^{61} +(-1.90479 - 2.62172i) q^{62} +(7.72561 + 1.16705i) q^{63} +(5.77574 + 4.19632i) q^{64} +(8.94935 - 2.41791i) q^{65} +(0.187663 + 1.78549i) q^{66} +(-1.81016 + 1.62988i) q^{67} +(-0.329902 + 0.190469i) q^{68} +(-0.362698 + 1.11627i) q^{69} +(1.73845 - 8.56674i) q^{70} +(-2.88907 - 8.89164i) q^{71} +(-5.89133 - 5.30458i) q^{72} +(0.425399 + 0.955462i) q^{73} +(-1.68408 + 2.91692i) q^{74} +(-0.873057 + 0.639871i) q^{75} +0.222736 q^{76} +(-11.4732 + 9.42747i) q^{77} +(1.26121 - 0.409792i) q^{78} +(-0.952485 + 1.05784i) q^{79} +(-6.83652 + 6.86498i) q^{80} +(5.74141 + 6.37648i) q^{81} +(1.02127 - 0.589633i) q^{82} +(-12.1826 - 3.95837i) q^{83} +(0.0156716 - 0.103742i) q^{84} +(1.67547 + 4.33779i) q^{85} +(0.640985 - 6.09856i) q^{86} +(0.324712 - 0.0341286i) q^{87} +(14.9844 - 1.57492i) q^{88} +(0.530946 - 5.05162i) q^{89} +(7.56978 - 6.15596i) q^{90} +(8.57341 + 6.84169i) q^{91} +(-0.944526 - 0.306895i) q^{92} +(-0.411193 + 0.237402i) q^{93} +(11.9972 + 13.3242i) q^{94} +(0.419758 - 2.68635i) q^{95} +(-0.149646 + 0.166198i) q^{96} +(9.10264 - 2.95763i) q^{97} +(9.38759 - 4.34153i) q^{98} -16.5749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.46946 + 0.154447i 1.03907 + 0.109210i 0.608666 0.793427i \(-0.291705\pi\)
0.430402 + 0.902637i \(0.358372\pi\)
\(3\) 0.0450101 0.211756i 0.0259866 0.122257i −0.963242 0.268634i \(-0.913428\pi\)
0.989229 + 0.146377i \(0.0467611\pi\)
\(4\) 0.179176 + 0.0380851i 0.0895880 + 0.0190425i
\(5\) 0.796997 2.08921i 0.356428 0.934323i
\(6\) 0.0988458 0.304216i 0.0403536 0.124196i
\(7\) 2.55064 0.703027i 0.964050 0.265719i
\(8\) −2.55307 0.829544i −0.902647 0.293288i
\(9\) 2.69782 + 1.20115i 0.899274 + 0.400383i
\(10\) 1.49383 2.94692i 0.472391 0.931899i
\(11\) −5.12740 + 2.28287i −1.54597 + 0.688310i −0.989761 0.142732i \(-0.954411\pi\)
−0.556209 + 0.831043i \(0.687745\pi\)
\(12\) 0.0161295 0.0362274i 0.00465618 0.0104579i
\(13\) 2.43682 + 3.35400i 0.675854 + 0.930233i 0.999875 0.0158171i \(-0.00503496\pi\)
−0.324021 + 0.946050i \(0.605035\pi\)
\(14\) 3.85665 0.639135i 1.03073 0.170816i
\(15\) −0.406529 0.262804i −0.104965 0.0678558i
\(16\) −3.95821 1.76231i −0.989553 0.440577i
\(17\) −1.54544 + 1.39152i −0.374825 + 0.337494i −0.834915 0.550378i \(-0.814483\pi\)
0.460091 + 0.887872i \(0.347817\pi\)
\(18\) 3.77884 + 2.18171i 0.890681 + 0.514235i
\(19\) 1.18938 0.252810i 0.272862 0.0579986i −0.0694484 0.997586i \(-0.522124\pi\)
0.342310 + 0.939587i \(0.388791\pi\)
\(20\) 0.222371 0.343983i 0.0497236 0.0769169i
\(21\) −0.0340657 0.571756i −0.00743374 0.124767i
\(22\) −7.88712 + 2.56268i −1.68154 + 0.546365i
\(23\) −5.39196 0.566717i −1.12430 0.118169i −0.475923 0.879487i \(-0.657886\pi\)
−0.648378 + 0.761318i \(0.724552\pi\)
\(24\) −0.290575 + 0.503290i −0.0593133 + 0.102734i
\(25\) −3.72959 3.33019i −0.745918 0.666038i
\(26\) 3.06281 + 5.30495i 0.600667 + 1.04039i
\(27\) 0.757522 1.04264i 0.145785 0.200656i
\(28\) 0.483788 0.0288245i 0.0914274 0.00544731i
\(29\) 0.466053 + 1.43436i 0.0865438 + 0.266355i 0.984958 0.172795i \(-0.0552798\pi\)
−0.898414 + 0.439150i \(0.855280\pi\)
\(30\) −0.556791 0.448969i −0.101656 0.0819702i
\(31\) −1.46756 1.62989i −0.263581 0.292736i 0.596798 0.802392i \(-0.296439\pi\)
−0.860378 + 0.509656i \(0.829773\pi\)
\(32\) −0.894649 0.516526i −0.158153 0.0913098i
\(33\) 0.252626 + 1.18851i 0.0439765 + 0.206893i
\(34\) −2.48589 + 1.80610i −0.426326 + 0.309744i
\(35\) 0.564081 5.88913i 0.0953471 0.995444i
\(36\) 0.437639 + 0.317964i 0.0729399 + 0.0529939i
\(37\) −0.927175 + 2.08247i −0.152427 + 0.342356i −0.973578 0.228355i \(-0.926665\pi\)
0.821151 + 0.570710i \(0.193332\pi\)
\(38\) 1.78679 0.187800i 0.289856 0.0304651i
\(39\) 0.819911 0.365048i 0.131291 0.0584545i
\(40\) −3.76788 + 4.67276i −0.595754 + 0.738828i
\(41\) 0.645691 0.469122i 0.100840 0.0732645i −0.536223 0.844077i \(-0.680149\pi\)
0.637063 + 0.770812i \(0.280149\pi\)
\(42\) 0.0382477 0.845436i 0.00590174 0.130454i
\(43\) 4.15020i 0.632899i −0.948609 0.316449i \(-0.897509\pi\)
0.948609 0.316449i \(-0.102491\pi\)
\(44\) −1.00565 + 0.213758i −0.151608 + 0.0322252i
\(45\) 4.65961 4.67900i 0.694613 0.697504i
\(46\) −7.83576 1.66554i −1.15532 0.245571i
\(47\) 9.01773 + 8.11960i 1.31537 + 1.18437i 0.969223 + 0.246186i \(0.0791773\pi\)
0.346148 + 0.938180i \(0.387489\pi\)
\(48\) −0.551339 + 0.758853i −0.0795790 + 0.109531i
\(49\) 6.01151 3.58633i 0.858787 0.512334i
\(50\) −4.96616 5.46962i −0.702321 0.773521i
\(51\) 0.225102 + 0.389889i 0.0315206 + 0.0545954i
\(52\) 0.308883 + 0.693764i 0.0428344 + 0.0962077i
\(53\) −2.22754 + 10.4798i −0.305976 + 1.43951i 0.509378 + 0.860543i \(0.329876\pi\)
−0.815354 + 0.578963i \(0.803458\pi\)
\(54\) 1.27418 1.41513i 0.173395 0.192574i
\(55\) 0.682859 + 12.5317i 0.0920767 + 1.68977i
\(56\) −7.09515 0.320986i −0.948130 0.0428935i
\(57\) 0.263237i 0.0348666i
\(58\) 0.463315 + 2.17973i 0.0608362 + 0.286212i
\(59\) −1.05882 10.0740i −0.137846 1.31152i −0.816622 0.577173i \(-0.804156\pi\)
0.678776 0.734346i \(-0.262511\pi\)
\(60\) −0.0628314 0.0625710i −0.00811150 0.00807788i
\(61\) 0.761635 7.24647i 0.0975173 0.927815i −0.830936 0.556367i \(-0.812195\pi\)
0.928454 0.371448i \(-0.121139\pi\)
\(62\) −1.90479 2.62172i −0.241909 0.332959i
\(63\) 7.72561 + 1.16705i 0.973335 + 0.147035i
\(64\) 5.77574 + 4.19632i 0.721968 + 0.524540i
\(65\) 8.94935 2.41791i 1.11003 0.299904i
\(66\) 0.187663 + 1.78549i 0.0230997 + 0.219779i
\(67\) −1.81016 + 1.62988i −0.221147 + 0.199121i −0.772256 0.635312i \(-0.780872\pi\)
0.551109 + 0.834433i \(0.314205\pi\)
\(68\) −0.329902 + 0.190469i −0.0400065 + 0.0230978i
\(69\) −0.362698 + 1.11627i −0.0436638 + 0.134383i
\(70\) 1.73845 8.56674i 0.207785 1.02392i
\(71\) −2.88907 8.89164i −0.342869 1.05524i −0.962715 0.270519i \(-0.912805\pi\)
0.619845 0.784724i \(-0.287195\pi\)
\(72\) −5.89133 5.30458i −0.694300 0.625150i
\(73\) 0.425399 + 0.955462i 0.0497892 + 0.111828i 0.936727 0.350060i \(-0.113839\pi\)
−0.886938 + 0.461888i \(0.847172\pi\)
\(74\) −1.68408 + 2.91692i −0.195771 + 0.339085i
\(75\) −0.873057 + 0.639871i −0.100812 + 0.0738859i
\(76\) 0.222736 0.0255496
\(77\) −11.4732 + 9.42747i −1.30750 + 1.07436i
\(78\) 1.26121 0.409792i 0.142804 0.0463998i
\(79\) −0.952485 + 1.05784i −0.107163 + 0.119016i −0.794340 0.607474i \(-0.792183\pi\)
0.687177 + 0.726490i \(0.258850\pi\)
\(80\) −6.83652 + 6.86498i −0.764346 + 0.767528i
\(81\) 5.74141 + 6.37648i 0.637934 + 0.708498i
\(82\) 1.02127 0.589633i 0.112781 0.0651140i
\(83\) −12.1826 3.95837i −1.33721 0.434487i −0.448842 0.893611i \(-0.648164\pi\)
−0.888372 + 0.459124i \(0.848164\pi\)
\(84\) 0.0156716 0.103742i 0.00170991 0.0113192i
\(85\) 1.67547 + 4.33779i 0.181730 + 0.470499i
\(86\) 0.640985 6.09856i 0.0691192 0.657625i
\(87\) 0.324712 0.0341286i 0.0348128 0.00365897i
\(88\) 14.9844 1.57492i 1.59734 0.167887i
\(89\) 0.530946 5.05162i 0.0562802 0.535470i −0.929666 0.368405i \(-0.879904\pi\)
0.985946 0.167066i \(-0.0534292\pi\)
\(90\) 7.56978 6.15596i 0.797925 0.648896i
\(91\) 8.57341 + 6.84169i 0.898738 + 0.717204i
\(92\) −0.944526 0.306895i −0.0984737 0.0319960i
\(93\) −0.411193 + 0.237402i −0.0426387 + 0.0246175i
\(94\) 11.9972 + 13.3242i 1.23742 + 1.37429i
\(95\) 0.419758 2.68635i 0.0430662 0.275613i
\(96\) −0.149646 + 0.166198i −0.0152731 + 0.0169626i
\(97\) 9.10264 2.95763i 0.924233 0.300301i 0.192031 0.981389i \(-0.438493\pi\)
0.732202 + 0.681087i \(0.238493\pi\)
\(98\) 9.38759 4.34153i 0.948290 0.438561i
\(99\) −16.5749 −1.66584
\(100\) −0.541423 0.738732i −0.0541423 0.0738732i
\(101\) 8.57674 14.8553i 0.853417 1.47816i −0.0246881 0.999695i \(-0.507859\pi\)
0.878105 0.478467i \(-0.158807\pi\)
\(102\) 0.270563 + 0.607694i 0.0267897 + 0.0601707i
\(103\) 1.94863 + 1.75456i 0.192004 + 0.172881i 0.759526 0.650477i \(-0.225431\pi\)
−0.567522 + 0.823359i \(0.692098\pi\)
\(104\) −3.43910 10.5845i −0.337231 1.03789i
\(105\) −1.22167 0.384518i −0.119223 0.0375251i
\(106\) −4.89186 + 15.0556i −0.475139 + 1.46233i
\(107\) −7.52810 + 4.34635i −0.727769 + 0.420178i −0.817605 0.575779i \(-0.804699\pi\)
0.0898366 + 0.995957i \(0.471366\pi\)
\(108\) 0.175439 0.157966i 0.0168816 0.0152003i
\(109\) −1.70676 16.2387i −0.163478 1.55539i −0.701631 0.712541i \(-0.747544\pi\)
0.538153 0.842847i \(-0.319122\pi\)
\(110\) −0.932038 + 18.5203i −0.0888664 + 1.76584i
\(111\) 0.399243 + 0.290067i 0.0378945 + 0.0275319i
\(112\) −11.3349 1.71228i −1.07105 0.161796i
\(113\) 3.45854 + 4.76028i 0.325352 + 0.447809i 0.940092 0.340921i \(-0.110739\pi\)
−0.614740 + 0.788730i \(0.710739\pi\)
\(114\) 0.0406561 0.386817i 0.00380779 0.0362287i
\(115\) −5.48137 + 10.8133i −0.511140 + 1.00834i
\(116\) 0.0288777 + 0.274753i 0.00268123 + 0.0255102i
\(117\) 2.54547 + 11.9755i 0.235329 + 1.10713i
\(118\) 14.9669i 1.37781i
\(119\) −2.96358 + 4.63575i −0.271671 + 0.424959i
\(120\) 0.819892 + 1.00819i 0.0748455 + 0.0920350i
\(121\) 13.7183 15.2358i 1.24712 1.38507i
\(122\) 2.23839 10.5308i 0.202654 0.953413i
\(123\) −0.0702767 0.157844i −0.00633664 0.0142323i
\(124\) −0.200877 0.347928i −0.0180393 0.0312449i
\(125\) −9.92993 + 5.13774i −0.888160 + 0.459534i
\(126\) 11.1723 + 2.90814i 0.995303 + 0.259077i
\(127\) 7.41853 10.2107i 0.658288 0.906055i −0.341135 0.940014i \(-0.610811\pi\)
0.999423 + 0.0339588i \(0.0108115\pi\)
\(128\) 9.37455 + 8.44089i 0.828601 + 0.746076i
\(129\) −0.878829 0.186801i −0.0773765 0.0164469i
\(130\) 13.5242 2.17083i 1.18615 0.190394i
\(131\) −3.32706 + 0.707188i −0.290686 + 0.0617873i −0.350947 0.936395i \(-0.614140\pi\)
0.0602605 + 0.998183i \(0.480807\pi\)
\(132\) 0.222574i 0.0193726i
\(133\) 2.85594 1.48099i 0.247641 0.128418i
\(134\) −2.91170 + 2.11547i −0.251532 + 0.182749i
\(135\) −1.57455 2.41360i −0.135516 0.207730i
\(136\) 5.09995 2.27064i 0.437317 0.194706i
\(137\) 13.5721 1.42648i 1.15954 0.121873i 0.494841 0.868983i \(-0.335226\pi\)
0.664700 + 0.747111i \(0.268560\pi\)
\(138\) −0.705377 + 1.58430i −0.0600457 + 0.134865i
\(139\) −5.59208 4.06288i −0.474314 0.344609i 0.324806 0.945781i \(-0.394701\pi\)
−0.799120 + 0.601171i \(0.794701\pi\)
\(140\) 0.325358 1.03371i 0.0274977 0.0873642i
\(141\) 2.12526 1.54409i 0.178979 0.130036i
\(142\) −2.87210 13.5122i −0.241021 1.13391i
\(143\) −20.1513 11.6344i −1.68514 0.972915i
\(144\) −8.56176 9.50880i −0.713480 0.792400i
\(145\) 3.36813 + 0.169502i 0.279708 + 0.0140764i
\(146\) 0.477540 + 1.46972i 0.0395215 + 0.121635i
\(147\) −0.488849 1.43439i −0.0403196 0.118307i
\(148\) −0.245439 + 0.337817i −0.0201749 + 0.0277684i
\(149\) 6.00186 + 10.3955i 0.491692 + 0.851635i 0.999954 0.00956709i \(-0.00304534\pi\)
−0.508262 + 0.861202i \(0.669712\pi\)
\(150\) −1.38175 + 0.805426i −0.112820 + 0.0657628i
\(151\) −8.59407 + 14.8854i −0.699375 + 1.21135i 0.269308 + 0.963054i \(0.413205\pi\)
−0.968683 + 0.248299i \(0.920128\pi\)
\(152\) −3.24628 0.341198i −0.263308 0.0276748i
\(153\) −5.84075 + 1.89777i −0.472196 + 0.153426i
\(154\) −18.3155 + 12.0813i −1.47591 + 0.973541i
\(155\) −4.57481 + 1.76702i −0.367458 + 0.141930i
\(156\) 0.160811 0.0341815i 0.0128752 0.00273671i
\(157\) −1.77467 1.02461i −0.141634 0.0817725i 0.427508 0.904011i \(-0.359391\pi\)
−0.569143 + 0.822239i \(0.692725\pi\)
\(158\) −1.56302 + 1.40735i −0.124347 + 0.111963i
\(159\) 2.11889 + 0.943390i 0.168039 + 0.0748157i
\(160\) −1.79216 + 1.45744i −0.141683 + 0.115221i
\(161\) −14.1513 + 2.34520i −1.11528 + 0.184828i
\(162\) 7.45196 + 10.2567i 0.585482 + 0.805846i
\(163\) −4.95453 + 11.1281i −0.388069 + 0.871616i 0.608858 + 0.793279i \(0.291628\pi\)
−0.996927 + 0.0783373i \(0.975039\pi\)
\(164\) 0.133559 0.0594642i 0.0104292 0.00464338i
\(165\) 2.68439 + 0.419452i 0.208979 + 0.0326543i
\(166\) −17.2905 7.69825i −1.34201 0.597500i
\(167\) 4.28292 + 1.39160i 0.331422 + 0.107686i 0.470001 0.882666i \(-0.344253\pi\)
−0.138579 + 0.990351i \(0.544253\pi\)
\(168\) −0.387324 + 1.48799i −0.0298827 + 0.114801i
\(169\) −1.29399 + 3.98249i −0.0995377 + 0.306346i
\(170\) 1.79208 + 6.63300i 0.137446 + 0.508728i
\(171\) 3.51239 + 0.746581i 0.268599 + 0.0570925i
\(172\) 0.158060 0.743616i 0.0120520 0.0567002i
\(173\) −24.9042 2.61753i −1.89343 0.199007i −0.914696 0.404143i \(-0.867570\pi\)
−0.978734 + 0.205135i \(0.934237\pi\)
\(174\) 0.482424 0.0365724
\(175\) −11.8540 5.87210i −0.896082 0.443889i
\(176\) 24.3185 1.83307
\(177\) −2.18088 0.229220i −0.163925 0.0172292i
\(178\) 1.56041 7.34117i 0.116958 0.550244i
\(179\) −6.40929 1.36234i −0.479053 0.101826i −0.0379449 0.999280i \(-0.512081\pi\)
−0.441108 + 0.897454i \(0.645414\pi\)
\(180\) 1.01309 0.660904i 0.0755113 0.0492609i
\(181\) −6.10225 + 18.7808i −0.453577 + 1.39597i 0.419221 + 0.907884i \(0.362303\pi\)
−0.872798 + 0.488082i \(0.837697\pi\)
\(182\) 11.5416 + 11.3778i 0.855524 + 0.843375i
\(183\) −1.50020 0.487445i −0.110898 0.0360330i
\(184\) 13.2959 + 5.91973i 0.980190 + 0.436409i
\(185\) 3.61176 + 3.59679i 0.265542 + 0.264441i
\(186\) −0.640899 + 0.285347i −0.0469930 + 0.0209226i
\(187\) 4.74744 10.6629i 0.347167 0.779750i
\(188\) 1.30653 + 1.79828i 0.0952882 + 0.131153i
\(189\) 1.19916 3.19196i 0.0872261 0.232181i
\(190\) 1.03172 3.88266i 0.0748486 0.281678i
\(191\) −13.9375 6.20539i −1.00848 0.449006i −0.165077 0.986281i \(-0.552787\pi\)
−0.843407 + 0.537275i \(0.819454\pi\)
\(192\) 1.14856 1.03417i 0.0828904 0.0746349i
\(193\) 2.97402 + 1.71705i 0.214075 + 0.123596i 0.603204 0.797587i \(-0.293891\pi\)
−0.389129 + 0.921183i \(0.627224\pi\)
\(194\) 13.8328 2.94025i 0.993137 0.211098i
\(195\) −0.109195 2.00391i −0.00781958 0.143503i
\(196\) 1.21370 0.413637i 0.0866931 0.0295455i
\(197\) −7.61009 + 2.47267i −0.542197 + 0.176170i −0.567295 0.823515i \(-0.692010\pi\)
0.0250984 + 0.999685i \(0.492010\pi\)
\(198\) −24.3562 2.55994i −1.73092 0.181927i
\(199\) −9.60469 + 16.6358i −0.680859 + 1.17928i 0.293860 + 0.955848i \(0.405060\pi\)
−0.974719 + 0.223434i \(0.928273\pi\)
\(200\) 6.75938 + 11.5961i 0.477960 + 0.819966i
\(201\) 0.263661 + 0.456674i 0.0185972 + 0.0322113i
\(202\) 14.8976 20.5048i 1.04819 1.44271i
\(203\) 2.19713 + 3.33089i 0.154208 + 0.233783i
\(204\) 0.0254840 + 0.0784318i 0.00178424 + 0.00549132i
\(205\) −0.465480 1.72287i −0.0325105 0.120331i
\(206\) 2.59246 + 2.87922i 0.180625 + 0.200604i
\(207\) −13.8658 8.00544i −0.963742 0.556416i
\(208\) −3.73468 17.5703i −0.258954 1.21828i
\(209\) −5.52128 + 4.01145i −0.381915 + 0.277478i
\(210\) −1.73581 0.753718i −0.119782 0.0520115i
\(211\) 15.3504 + 11.1527i 1.05676 + 0.767784i 0.973487 0.228742i \(-0.0734612\pi\)
0.0832775 + 0.996526i \(0.473461\pi\)
\(212\) −0.798244 + 1.79289i −0.0548237 + 0.123136i
\(213\) −2.01289 + 0.211564i −0.137921 + 0.0144961i
\(214\) −11.7336 + 5.22411i −0.802089 + 0.357113i
\(215\) −8.67063 3.30770i −0.591332 0.225583i
\(216\) −2.79893 + 2.03354i −0.190443 + 0.138365i
\(217\) −4.88906 3.12552i −0.331891 0.212174i
\(218\) 24.1258i 1.63401i
\(219\) 0.221472 0.0470753i 0.0149657 0.00318105i
\(220\) −0.354917 + 2.27138i −0.0239285 + 0.153136i
\(221\) −8.43313 1.79252i −0.567274 0.120578i
\(222\) 0.541873 + 0.487905i 0.0363682 + 0.0327460i
\(223\) 9.06575 12.4779i 0.607088 0.835585i −0.389246 0.921134i \(-0.627264\pi\)
0.996334 + 0.0855491i \(0.0272645\pi\)
\(224\) −2.64506 0.688508i −0.176730 0.0460029i
\(225\) −6.06172 13.4640i −0.404115 0.897603i
\(226\) 4.34700 + 7.52922i 0.289158 + 0.500836i
\(227\) 4.60801 + 10.3498i 0.305844 + 0.686938i 0.999441 0.0334257i \(-0.0106417\pi\)
−0.693597 + 0.720363i \(0.743975\pi\)
\(228\) 0.0100254 0.0471657i 0.000663947 0.00312363i
\(229\) 3.12389 3.46944i 0.206433 0.229267i −0.631034 0.775755i \(-0.717369\pi\)
0.837467 + 0.546489i \(0.184036\pi\)
\(230\) −9.72475 + 15.0431i −0.641231 + 0.991913i
\(231\) 1.47991 + 2.85386i 0.0973710 + 0.187770i
\(232\) 4.04864i 0.265806i
\(233\) −1.12681 5.30122i −0.0738197 0.347294i 0.925701 0.378256i \(-0.123476\pi\)
−0.999521 + 0.0309621i \(0.990143\pi\)
\(234\) 1.89090 + 17.9907i 0.123612 + 1.17609i
\(235\) 24.1507 12.3686i 1.57541 0.806840i
\(236\) 0.193953 1.84534i 0.0126253 0.120121i
\(237\) 0.181133 + 0.249308i 0.0117658 + 0.0161943i
\(238\) −5.07086 + 6.35436i −0.328695 + 0.411892i
\(239\) 9.08463 + 6.60037i 0.587636 + 0.426942i 0.841469 0.540306i \(-0.181691\pi\)
−0.253833 + 0.967248i \(0.581691\pi\)
\(240\) 1.14599 + 1.75667i 0.0739732 + 0.113392i
\(241\) 2.40127 + 22.8465i 0.154679 + 1.47168i 0.746381 + 0.665518i \(0.231790\pi\)
−0.591702 + 0.806157i \(0.701544\pi\)
\(242\) 22.5117 20.2697i 1.44711 1.30298i
\(243\) 4.95701 2.86193i 0.317992 0.183593i
\(244\) 0.412449 1.26939i 0.0264043 0.0812642i
\(245\) −2.70145 15.4176i −0.172589 0.984994i
\(246\) −0.0788906 0.242800i −0.00502988 0.0154804i
\(247\) 3.74623 + 3.37312i 0.238367 + 0.214626i
\(248\) 2.39471 + 5.37862i 0.152065 + 0.341543i
\(249\) −1.38655 + 2.40157i −0.0878689 + 0.152193i
\(250\) −15.3852 + 6.01608i −0.973045 + 0.380490i
\(251\) 28.9587 1.82786 0.913928 0.405877i \(-0.133034\pi\)
0.913928 + 0.405877i \(0.133034\pi\)
\(252\) 1.33980 + 0.503338i 0.0843993 + 0.0317073i
\(253\) 28.9405 9.40333i 1.81947 0.591182i
\(254\) 12.4783 13.8585i 0.782957 0.869561i
\(255\) 0.993965 0.159546i 0.0622445 0.00999114i
\(256\) 2.91777 + 3.24051i 0.182361 + 0.202532i
\(257\) 21.0760 12.1682i 1.31469 0.759034i 0.331817 0.943344i \(-0.392338\pi\)
0.982868 + 0.184310i \(0.0590051\pi\)
\(258\) −1.26256 0.410229i −0.0786033 0.0255398i
\(259\) −0.900856 + 5.96346i −0.0559764 + 0.370551i
\(260\) 1.69560 0.0923943i 0.105156 0.00573005i
\(261\) −0.465554 + 4.42945i −0.0288171 + 0.274176i
\(262\) −4.99821 + 0.525333i −0.308791 + 0.0324552i
\(263\) −4.37652 + 0.459991i −0.269868 + 0.0283643i −0.238496 0.971143i \(-0.576654\pi\)
−0.0313721 + 0.999508i \(0.509988\pi\)
\(264\) 0.340949 3.24392i 0.0209840 0.199649i
\(265\) 20.1191 + 13.0061i 1.23590 + 0.798961i
\(266\) 4.42543 1.73517i 0.271341 0.106390i
\(267\) −1.04581 0.339805i −0.0640026 0.0207957i
\(268\) −0.386412 + 0.223095i −0.0236039 + 0.0136277i
\(269\) −13.0738 14.5199i −0.797124 0.885296i 0.198369 0.980127i \(-0.436436\pi\)
−0.995493 + 0.0948313i \(0.969769\pi\)
\(270\) −1.94097 3.78989i −0.118124 0.230645i
\(271\) 15.1780 16.8568i 0.921996 1.02398i −0.0776396 0.996981i \(-0.524738\pi\)
0.999635 0.0269987i \(-0.00859499\pi\)
\(272\) 8.56948 2.78439i 0.519601 0.168829i
\(273\) 1.83466 1.50753i 0.111039 0.0912396i
\(274\) 20.1640 1.21815
\(275\) 26.7255 + 8.56106i 1.61161 + 0.516251i
\(276\) −0.107500 + 0.186196i −0.00647075 + 0.0112077i
\(277\) −3.48953 7.83761i −0.209666 0.470916i 0.777848 0.628453i \(-0.216311\pi\)
−0.987513 + 0.157536i \(0.949645\pi\)
\(278\) −7.58986 6.83394i −0.455209 0.409872i
\(279\) −2.00147 6.15989i −0.119825 0.368783i
\(280\) −6.32543 + 14.5674i −0.378017 + 0.870571i
\(281\) 2.65602 8.17439i 0.158445 0.487643i −0.840049 0.542511i \(-0.817474\pi\)
0.998494 + 0.0548676i \(0.0174737\pi\)
\(282\) 3.36148 1.94075i 0.200173 0.115570i
\(283\) −11.5848 + 10.4310i −0.688643 + 0.620057i −0.937295 0.348536i \(-0.886679\pi\)
0.248653 + 0.968593i \(0.420012\pi\)
\(284\) −0.179013 1.70320i −0.0106225 0.101066i
\(285\) −0.549956 0.209799i −0.0325766 0.0124274i
\(286\) −27.8148 20.2086i −1.64472 1.19496i
\(287\) 1.31712 1.65050i 0.0777470 0.0974258i
\(288\) −1.79318 2.46810i −0.105664 0.145434i
\(289\) −1.32493 + 12.6058i −0.0779369 + 0.741520i
\(290\) 4.92316 + 0.769274i 0.289098 + 0.0451733i
\(291\) −0.216584 2.06066i −0.0126964 0.120798i
\(292\) 0.0398325 + 0.187397i 0.00233102 + 0.0109666i
\(293\) 33.2953i 1.94513i 0.232624 + 0.972567i \(0.425269\pi\)
−0.232624 + 0.972567i \(0.574731\pi\)
\(294\) −0.496809 2.18329i −0.0289745 0.127332i
\(295\) −21.8905 5.81684i −1.27451 0.338669i
\(296\) 4.09465 4.54756i 0.237996 0.264322i
\(297\) −1.50391 + 7.07536i −0.0872659 + 0.410554i
\(298\) 7.21397 + 16.2028i 0.417894 + 0.938605i
\(299\) −11.2385 19.4656i −0.649938 1.12573i
\(300\) −0.180800 + 0.0813991i −0.0104385 + 0.00469958i
\(301\) −2.91770 10.5856i −0.168173 0.610147i
\(302\) −14.9277 + 20.5462i −0.858991 + 1.18230i
\(303\) −2.75967 2.48482i −0.158539 0.142749i
\(304\) −5.15334 1.09538i −0.295564 0.0628241i
\(305\) −14.5324 7.36663i −0.832121 0.421812i
\(306\) −8.87587 + 1.88663i −0.507400 + 0.107851i
\(307\) 14.3799i 0.820703i 0.911927 + 0.410351i \(0.134594\pi\)
−0.911927 + 0.410351i \(0.865406\pi\)
\(308\) −2.41477 + 1.25222i −0.137595 + 0.0713518i
\(309\) 0.459246 0.333661i 0.0261256 0.0189813i
\(310\) −6.99543 + 1.89000i −0.397314 + 0.107345i
\(311\) 22.9079 10.1993i 1.29899 0.578347i 0.363464 0.931608i \(-0.381594\pi\)
0.935525 + 0.353262i \(0.114927\pi\)
\(312\) −2.39612 + 0.251842i −0.135653 + 0.0142577i
\(313\) −1.86589 + 4.19086i −0.105467 + 0.236882i −0.958568 0.284863i \(-0.908052\pi\)
0.853102 + 0.521745i \(0.174719\pi\)
\(314\) −2.44957 1.77972i −0.138237 0.100435i
\(315\) 8.59550 15.2103i 0.484302 0.857002i
\(316\) −0.210950 + 0.153264i −0.0118669 + 0.00862180i
\(317\) 3.86671 + 18.1914i 0.217176 + 1.02173i 0.942727 + 0.333565i \(0.108252\pi\)
−0.725551 + 0.688168i \(0.758415\pi\)
\(318\) 2.96793 + 1.71353i 0.166433 + 0.0960902i
\(319\) −5.66410 6.29062i −0.317129 0.352207i
\(320\) 13.3703 8.72228i 0.747420 0.487590i
\(321\) 0.581525 + 1.78975i 0.0324576 + 0.0998941i
\(322\) −21.1571 + 1.26056i −1.17904 + 0.0702481i
\(323\) −1.48632 + 2.04575i −0.0827012 + 0.113828i
\(324\) 0.785874 + 1.36117i 0.0436597 + 0.0756208i
\(325\) 2.08110 20.6241i 0.115439 1.14402i
\(326\) −8.99919 + 15.5871i −0.498419 + 0.863288i
\(327\) −3.51547 0.369491i −0.194406 0.0204329i
\(328\) −2.03765 + 0.662073i −0.112510 + 0.0365569i
\(329\) 28.7093 + 14.3705i 1.58279 + 0.792269i
\(330\) 3.87983 + 1.03096i 0.213578 + 0.0567527i
\(331\) −20.9992 + 4.46351i −1.15422 + 0.245337i −0.744977 0.667090i \(-0.767540\pi\)
−0.409241 + 0.912426i \(0.634206\pi\)
\(332\) −2.03208 1.17322i −0.111525 0.0643888i
\(333\) −5.00271 + 4.50446i −0.274147 + 0.246843i
\(334\) 6.07867 + 2.70640i 0.332610 + 0.148087i
\(335\) 1.96246 + 5.08082i 0.107221 + 0.277595i
\(336\) −0.872772 + 2.32317i −0.0476136 + 0.126739i
\(337\) −3.01712 4.15270i −0.164353 0.226212i 0.718895 0.695119i \(-0.244648\pi\)
−0.883248 + 0.468906i \(0.844648\pi\)
\(338\) −2.51656 + 5.65228i −0.136883 + 0.307443i
\(339\) 1.16369 0.518107i 0.0632028 0.0281397i
\(340\) 0.134999 + 0.841038i 0.00732133 + 0.0456117i
\(341\) 11.2456 + 5.00685i 0.608981 + 0.271136i
\(342\) 5.04602 + 1.63955i 0.272858 + 0.0886568i
\(343\) 12.8119 13.3737i 0.691777 0.722112i
\(344\) −3.44277 + 10.5958i −0.185622 + 0.571285i
\(345\) 2.04305 + 1.64742i 0.109994 + 0.0886940i
\(346\) −36.1915 7.69275i −1.94567 0.413565i
\(347\) 1.25386 5.89893i 0.0673105 0.316671i −0.931592 0.363505i \(-0.881580\pi\)
0.998903 + 0.0468341i \(0.0149132\pi\)
\(348\) 0.0594804 + 0.00625164i 0.00318848 + 0.000335123i
\(349\) 4.89281 0.261906 0.130953 0.991389i \(-0.458196\pi\)
0.130953 + 0.991389i \(0.458196\pi\)
\(350\) −16.5122 10.4597i −0.882613 0.559093i
\(351\) 5.34297 0.285186
\(352\) 5.76639 + 0.606072i 0.307349 + 0.0323037i
\(353\) 4.87689 22.9440i 0.259571 1.22118i −0.634381 0.773020i \(-0.718745\pi\)
0.893952 0.448163i \(-0.147922\pi\)
\(354\) −3.16932 0.673660i −0.168448 0.0358046i
\(355\) −20.8791 1.05074i −1.10815 0.0557677i
\(356\) 0.287524 0.884908i 0.0152387 0.0469000i
\(357\) 0.848257 + 0.836212i 0.0448945 + 0.0442570i
\(358\) −9.20782 2.99180i −0.486648 0.158122i
\(359\) −22.4575 9.99874i −1.18526 0.527713i −0.283093 0.959092i \(-0.591361\pi\)
−0.902171 + 0.431379i \(0.858027\pi\)
\(360\) −15.7777 + 8.08049i −0.831560 + 0.425879i
\(361\) −16.0067 + 7.12662i −0.842456 + 0.375085i
\(362\) −11.8677 + 26.6552i −0.623751 + 1.40097i
\(363\) −2.60880 3.59070i −0.136926 0.188463i
\(364\) 1.27558 + 1.55239i 0.0668588 + 0.0813671i
\(365\) 2.33520 0.127247i 0.122230 0.00666041i
\(366\) −2.12921 0.947984i −0.111295 0.0495519i
\(367\) −9.89946 + 8.91352i −0.516748 + 0.465282i −0.885761 0.464142i \(-0.846363\pi\)
0.369013 + 0.929424i \(0.379696\pi\)
\(368\) 20.3438 + 11.7455i 1.06049 + 0.612276i
\(369\) 2.30544 0.490037i 0.120017 0.0255103i
\(370\) 4.75184 + 5.84317i 0.247036 + 0.303772i
\(371\) 1.68590 + 28.2961i 0.0875277 + 1.46906i
\(372\) −0.0827174 + 0.0268765i −0.00428870 + 0.00139348i
\(373\) 10.8692 + 1.14240i 0.562787 + 0.0591513i 0.381651 0.924307i \(-0.375356\pi\)
0.181137 + 0.983458i \(0.442022\pi\)
\(374\) 8.62305 14.9356i 0.445887 0.772300i
\(375\) 0.641000 + 2.33397i 0.0331011 + 0.120526i
\(376\) −16.2874 28.2105i −0.839956 1.45485i
\(377\) −3.67517 + 5.05843i −0.189281 + 0.260523i
\(378\) 2.25511 4.50526i 0.115990 0.231726i
\(379\) 6.12263 + 18.8435i 0.314498 + 0.967926i 0.975960 + 0.217948i \(0.0699362\pi\)
−0.661462 + 0.749978i \(0.730064\pi\)
\(380\) 0.177520 0.465343i 0.00910659 0.0238716i
\(381\) −1.82827 2.03050i −0.0936653 0.104026i
\(382\) −19.5223 11.2712i −0.998847 0.576685i
\(383\) 2.15499 + 10.1384i 0.110115 + 0.518050i 0.998285 + 0.0585358i \(0.0186432\pi\)
−0.888170 + 0.459514i \(0.848023\pi\)
\(384\) 2.20936 1.60519i 0.112746 0.0819146i
\(385\) 10.5518 + 31.4836i 0.537771 + 1.60456i
\(386\) 4.10502 + 2.98248i 0.208940 + 0.151804i
\(387\) 4.98500 11.1965i 0.253402 0.569150i
\(388\) 1.74362 0.183262i 0.0885187 0.00930369i
\(389\) −6.16125 + 2.74316i −0.312388 + 0.139084i −0.556941 0.830552i \(-0.688025\pi\)
0.244554 + 0.969636i \(0.421359\pi\)
\(390\) 0.149040 2.96154i 0.00754694 0.149963i
\(391\) 9.12155 6.62719i 0.461297 0.335152i
\(392\) −18.3228 + 4.16937i −0.925443 + 0.210585i
\(393\) 0.736355i 0.0371442i
\(394\) −11.5647 + 2.45814i −0.582619 + 0.123839i
\(395\) 1.45092 + 2.83304i 0.0730039 + 0.142546i
\(396\) −2.96982 0.631255i −0.149239 0.0317218i
\(397\) −10.0788 9.07496i −0.505839 0.455459i 0.376267 0.926511i \(-0.377208\pi\)
−0.882105 + 0.471052i \(0.843874\pi\)
\(398\) −16.6831 + 22.9623i −0.836248 + 1.15100i
\(399\) −0.185063 0.671421i −0.00926471 0.0336131i
\(400\) 8.89369 + 19.7543i 0.444684 + 0.987714i
\(401\) 2.71139 + 4.69626i 0.135400 + 0.234520i 0.925750 0.378136i \(-0.123435\pi\)
−0.790350 + 0.612655i \(0.790101\pi\)
\(402\) 0.316908 + 0.711787i 0.0158059 + 0.0355007i
\(403\) 1.89046 8.89393i 0.0941707 0.443038i
\(404\) 2.10251 2.33508i 0.104604 0.116174i
\(405\) 17.8977 6.91296i 0.889343 0.343508i
\(406\) 2.71415 + 5.23397i 0.134701 + 0.259757i
\(407\) 12.7943i 0.634189i
\(408\) −0.251273 1.18215i −0.0124399 0.0585250i
\(409\) 0.510977 + 4.86162i 0.0252662 + 0.240392i 0.999865 + 0.0164337i \(0.00523123\pi\)
−0.974599 + 0.223958i \(0.928102\pi\)
\(410\) −0.417913 2.60359i −0.0206393 0.128582i
\(411\) 0.308815 2.93817i 0.0152327 0.144929i
\(412\) 0.282326 + 0.388588i 0.0139092 + 0.0191444i
\(413\) −9.78293 24.9507i −0.481386 1.22774i
\(414\) −19.1389 13.9052i −0.940627 0.683405i
\(415\) −17.9794 + 22.2972i −0.882572 + 1.09453i
\(416\) −0.447674 4.25934i −0.0219490 0.208831i
\(417\) −1.11204 + 1.00128i −0.0544568 + 0.0490331i
\(418\) −8.73289 + 5.04193i −0.427139 + 0.246609i
\(419\) 5.58541 17.1901i 0.272865 0.839793i −0.716911 0.697165i \(-0.754445\pi\)
0.989776 0.142628i \(-0.0455554\pi\)
\(420\) −0.204249 0.115424i −0.00996635 0.00563210i
\(421\) −5.45044 16.7747i −0.265638 0.817551i −0.991546 0.129758i \(-0.958580\pi\)
0.725907 0.687793i \(-0.241420\pi\)
\(422\) 20.8343 + 18.7593i 1.01420 + 0.913190i
\(423\) 14.5754 + 32.7369i 0.708680 + 1.59172i
\(424\) 14.3805 24.9077i 0.698378 1.20963i
\(425\) 10.3979 0.0431940i 0.504372 0.00209522i
\(426\) −2.99055 −0.144893
\(427\) −3.15181 19.0186i −0.152527 0.920373i
\(428\) −1.51439 + 0.492054i −0.0732006 + 0.0237843i
\(429\) −3.37066 + 3.74350i −0.162737 + 0.180738i
\(430\) −12.2303 6.19969i −0.589798 0.298976i
\(431\) −1.35906 1.50939i −0.0654636 0.0727047i 0.709523 0.704682i \(-0.248910\pi\)
−0.774987 + 0.631977i \(0.782244\pi\)
\(432\) −4.83589 + 2.79200i −0.232667 + 0.134330i
\(433\) 31.5673 + 10.2568i 1.51703 + 0.492912i 0.944930 0.327272i \(-0.106129\pi\)
0.572099 + 0.820185i \(0.306129\pi\)
\(434\) −6.70157 5.34793i −0.321686 0.256709i
\(435\) 0.187493 0.705592i 0.00898959 0.0338305i
\(436\) 0.312642 2.97459i 0.0149729 0.142457i
\(437\) −6.55634 + 0.689099i −0.313632 + 0.0329641i
\(438\) 0.332716 0.0349698i 0.0158978 0.00167092i
\(439\) 1.24151 11.8122i 0.0592540 0.563764i −0.924111 0.382124i \(-0.875193\pi\)
0.983365 0.181640i \(-0.0581406\pi\)
\(440\) 8.65216 32.5607i 0.412476 1.55227i
\(441\) 20.5257 2.45459i 0.977414 0.116885i
\(442\) −12.1153 3.93651i −0.576268 0.187241i
\(443\) 22.6341 13.0678i 1.07538 0.620870i 0.145732 0.989324i \(-0.453446\pi\)
0.929646 + 0.368454i \(0.120113\pi\)
\(444\) 0.0604876 + 0.0671783i 0.00287061 + 0.00318814i
\(445\) −10.1307 5.13538i −0.480242 0.243440i
\(446\) 15.2490 16.9357i 0.722060 0.801929i
\(447\) 2.47146 0.803026i 0.116896 0.0379818i
\(448\) 17.6820 + 6.64280i 0.835394 + 0.313843i
\(449\) 13.4885 0.636560 0.318280 0.947997i \(-0.396895\pi\)
0.318280 + 0.947997i \(0.396895\pi\)
\(450\) −6.82800 20.7211i −0.321875 0.976804i
\(451\) −2.23977 + 3.87940i −0.105467 + 0.182674i
\(452\) 0.438393 + 0.984647i 0.0206203 + 0.0463139i
\(453\) 2.76524 + 2.48984i 0.129922 + 0.116983i
\(454\) 5.17282 + 15.9203i 0.242772 + 0.747176i
\(455\) 21.1267 12.4588i 0.990435 0.584079i
\(456\) −0.218366 + 0.672062i −0.0102259 + 0.0314722i
\(457\) −16.7954 + 9.69680i −0.785653 + 0.453597i −0.838430 0.545009i \(-0.816526\pi\)
0.0527767 + 0.998606i \(0.483193\pi\)
\(458\) 5.12629 4.61574i 0.239536 0.215679i
\(459\) 0.280150 + 2.66545i 0.0130763 + 0.124412i
\(460\) −1.39395 + 1.72872i −0.0649934 + 0.0806019i
\(461\) −26.2530 19.0739i −1.22272 0.888360i −0.226399 0.974035i \(-0.572695\pi\)
−0.996323 + 0.0856749i \(0.972695\pi\)
\(462\) 1.73391 + 4.42221i 0.0806687 + 0.205740i
\(463\) 6.72009 + 9.24941i 0.312309 + 0.429857i 0.936100 0.351735i \(-0.114408\pi\)
−0.623791 + 0.781592i \(0.714408\pi\)
\(464\) 0.683056 6.49884i 0.0317101 0.301701i
\(465\) 0.168263 + 1.04828i 0.00780303 + 0.0486127i
\(466\) −0.837048 7.96398i −0.0387755 0.368924i
\(467\) 4.85706 + 22.8507i 0.224758 + 1.05740i 0.935329 + 0.353778i \(0.115103\pi\)
−0.710572 + 0.703625i \(0.751564\pi\)
\(468\) 2.24266i 0.103667i
\(469\) −3.47122 + 5.42982i −0.160286 + 0.250726i
\(470\) 37.3988 14.4453i 1.72508 0.666310i
\(471\) −0.296845 + 0.329679i −0.0136779 + 0.0151908i
\(472\) −5.65356 + 26.5979i −0.260226 + 1.22427i
\(473\) 9.47434 + 21.2797i 0.435631 + 0.978443i
\(474\) 0.227663 + 0.394324i 0.0104569 + 0.0181119i
\(475\) −5.27779 3.01797i −0.242162 0.138474i
\(476\) −0.707556 + 0.717748i −0.0324308 + 0.0328979i
\(477\) −18.5972 + 25.5969i −0.851509 + 1.17200i
\(478\) 12.3301 + 11.1021i 0.563967 + 0.507798i
\(479\) 36.8065 + 7.82347i 1.68173 + 0.357463i 0.947084 0.320985i \(-0.104014\pi\)
0.734648 + 0.678448i \(0.237347\pi\)
\(480\) 0.227956 + 0.445101i 0.0104047 + 0.0203160i
\(481\) −9.24397 + 1.96487i −0.421489 + 0.0895902i
\(482\) 33.9430i 1.54606i
\(483\) −0.140344 + 3.10219i −0.00638585 + 0.141154i
\(484\) 3.03825 2.20742i 0.138102 0.100337i
\(485\) 1.07568 21.3745i 0.0488441 0.970568i
\(486\) 7.72617 3.43991i 0.350466 0.156038i
\(487\) 8.94711 0.940379i 0.405432 0.0426126i 0.100382 0.994949i \(-0.467993\pi\)
0.305050 + 0.952336i \(0.401327\pi\)
\(488\) −7.95577 + 17.8690i −0.360141 + 0.808889i
\(489\) 2.13343 + 1.55003i 0.0964769 + 0.0700946i
\(490\) −1.58848 23.0728i −0.0717604 1.04232i
\(491\) −14.8610 + 10.7971i −0.670666 + 0.487267i −0.870248 0.492614i \(-0.836042\pi\)
0.199582 + 0.979881i \(0.436042\pi\)
\(492\) −0.00658040 0.0309584i −0.000296668 0.00139571i
\(493\) −2.71620 1.56820i −0.122332 0.0706282i
\(494\) 4.98398 + 5.53527i 0.224240 + 0.249044i
\(495\) −13.2101 + 34.6284i −0.593751 + 1.55643i
\(496\) 2.93653 + 9.03772i 0.131854 + 0.405806i
\(497\) −13.6200 20.6483i −0.610942 0.926201i
\(498\) −2.40840 + 3.31488i −0.107923 + 0.148543i
\(499\) −11.4708 19.8680i −0.513502 0.889412i −0.999877 0.0156617i \(-0.995015\pi\)
0.486375 0.873750i \(-0.338319\pi\)
\(500\) −1.97488 + 0.542378i −0.0883192 + 0.0242559i
\(501\) 0.487455 0.844297i 0.0217779 0.0377204i
\(502\) 42.5537 + 4.47258i 1.89927 + 0.199621i
\(503\) −2.48353 + 0.806947i −0.110735 + 0.0359800i −0.363860 0.931453i \(-0.618541\pi\)
0.253125 + 0.967433i \(0.418541\pi\)
\(504\) −18.7559 9.38829i −0.835455 0.418188i
\(505\) −24.2003 29.7583i −1.07690 1.32423i
\(506\) 43.9793 9.34809i 1.95512 0.415573i
\(507\) 0.785074 + 0.453263i 0.0348664 + 0.0201301i
\(508\) 1.71810 1.54698i 0.0762283 0.0686363i
\(509\) 9.26406 + 4.12463i 0.410622 + 0.182821i 0.601643 0.798765i \(-0.294513\pi\)
−0.191021 + 0.981586i \(0.561180\pi\)
\(510\) 1.48524 0.0809317i 0.0657674 0.00358372i
\(511\) 1.75675 + 2.13797i 0.0777142 + 0.0945782i
\(512\) −11.0424 15.1986i −0.488010 0.671688i
\(513\) 0.637390 1.43160i 0.0281415 0.0632068i
\(514\) 32.8498 14.6257i 1.44894 0.645110i
\(515\) 5.21869 2.67272i 0.229963 0.117774i
\(516\) −0.150351 0.0669405i −0.00661882 0.00294689i
\(517\) −64.7735 21.0462i −2.84874 0.925610i
\(518\) −2.24481 + 8.62395i −0.0986314 + 0.378915i
\(519\) −1.67522 + 5.15579i −0.0735339 + 0.226314i
\(520\) −24.8541 1.25079i −1.08992 0.0548507i
\(521\) −26.7941 5.69525i −1.17387 0.249514i −0.420612 0.907240i \(-0.638185\pi\)
−0.753256 + 0.657727i \(0.771518\pi\)
\(522\) −1.36823 + 6.43702i −0.0598858 + 0.281741i
\(523\) 1.75335 + 0.184284i 0.0766685 + 0.00805819i 0.142785 0.989754i \(-0.454394\pi\)
−0.0661165 + 0.997812i \(0.521061\pi\)
\(524\) −0.623062 −0.0272186
\(525\) −1.77700 + 2.24586i −0.0775548 + 0.0980174i
\(526\) −6.50219 −0.283509
\(527\) 4.53604 + 0.476757i 0.197593 + 0.0207679i
\(528\) 1.09458 5.14958i 0.0476354 0.224107i
\(529\) 6.25463 + 1.32946i 0.271940 + 0.0578027i
\(530\) 27.5555 + 22.2194i 1.19693 + 0.965149i
\(531\) 9.24382 28.4496i 0.401148 1.23461i
\(532\) 0.568119 0.156590i 0.0246311 0.00678902i
\(533\) 3.14687 + 1.02248i 0.136306 + 0.0442885i
\(534\) −1.48430 0.660853i −0.0642320 0.0285979i
\(535\) 3.08056 + 19.1918i 0.133184 + 0.829734i
\(536\) 5.97353 2.65959i 0.258017 0.114877i
\(537\) −0.576966 + 1.29589i −0.0248979 + 0.0559216i
\(538\) −16.9689 23.3557i −0.731583 1.00694i
\(539\) −22.6363 + 32.1121i −0.975014 + 1.38316i
\(540\) −0.190199 0.492427i −0.00818488 0.0211907i
\(541\) −25.4091 11.3129i −1.09242 0.486378i −0.220184 0.975458i \(-0.570666\pi\)
−0.872239 + 0.489080i \(0.837333\pi\)
\(542\) 24.9070 22.4263i 1.06985 0.963294i
\(543\) 3.70228 + 2.13751i 0.158880 + 0.0917295i
\(544\) 2.10138 0.446663i 0.0900961 0.0191505i
\(545\) −35.2864 9.37645i −1.51150 0.401643i
\(546\) 2.92880 1.93190i 0.125341 0.0826776i
\(547\) 16.6559 5.41183i 0.712154 0.231393i 0.0695360 0.997579i \(-0.477848\pi\)
0.642618 + 0.766186i \(0.277848\pi\)
\(548\) 2.48612 + 0.261302i 0.106202 + 0.0111623i
\(549\) 10.7588 18.6348i 0.459176 0.795316i
\(550\) 37.9499 + 16.7078i 1.61819 + 0.712425i
\(551\) 0.916934 + 1.58818i 0.0390627 + 0.0676586i
\(552\) 1.85199 2.54905i 0.0788259 0.108495i
\(553\) −1.68575 + 3.36779i −0.0716855 + 0.143213i
\(554\) −3.91724 12.0560i −0.166428 0.512212i
\(555\) 0.924207 0.602920i 0.0392304 0.0255925i
\(556\) −0.847232 0.940946i −0.0359306 0.0399050i
\(557\) 5.64693 + 3.26026i 0.239268 + 0.138141i 0.614840 0.788652i \(-0.289220\pi\)
−0.375572 + 0.926793i \(0.622554\pi\)
\(558\) −1.98971 9.36086i −0.0842313 0.396277i
\(559\) 13.9198 10.1133i 0.588743 0.427747i
\(560\) −12.6112 + 22.3163i −0.532921 + 0.943037i
\(561\) −2.04426 1.48524i −0.0863085 0.0627068i
\(562\) 5.16544 11.6018i 0.217891 0.489391i
\(563\) 13.8252 1.45309i 0.582663 0.0612403i 0.191388 0.981514i \(-0.438701\pi\)
0.391274 + 0.920274i \(0.372034\pi\)
\(564\) 0.439603 0.195724i 0.0185106 0.00824146i
\(565\) 12.7017 3.43169i 0.534363 0.144372i
\(566\) −18.6344 + 13.5387i −0.783264 + 0.569074i
\(567\) 19.1271 + 12.2277i 0.803262 + 0.513516i
\(568\) 25.0976i 1.05307i
\(569\) 22.9067 4.86896i 0.960297 0.204117i 0.299010 0.954250i \(-0.403344\pi\)
0.661287 + 0.750133i \(0.270010\pi\)
\(570\) −0.775739 0.393231i −0.0324921 0.0164706i
\(571\) 15.5857 + 3.31283i 0.652239 + 0.138638i 0.522135 0.852863i \(-0.325136\pi\)
0.130104 + 0.991500i \(0.458469\pi\)
\(572\) −3.16754 2.85207i −0.132441 0.119251i
\(573\) −1.94136 + 2.67205i −0.0811013 + 0.111626i
\(574\) 2.19037 2.22192i 0.0914243 0.0927412i
\(575\) 18.2225 + 20.0699i 0.759931 + 0.836971i
\(576\) 10.5415 + 18.2585i 0.439230 + 0.760769i
\(577\) 5.28934 + 11.8801i 0.220198 + 0.494573i 0.989539 0.144265i \(-0.0460819\pi\)
−0.769341 + 0.638838i \(0.779415\pi\)
\(578\) −3.89387 + 18.3192i −0.161964 + 0.761978i
\(579\) 0.497457 0.552482i 0.0206736 0.0229604i
\(580\) 0.597032 + 0.158646i 0.0247904 + 0.00658742i
\(581\) −33.8563 1.53166i −1.40459 0.0635441i
\(582\) 3.06152i 0.126904i
\(583\) −12.5024 58.8191i −0.517796 2.43604i
\(584\) −0.293477 2.79225i −0.0121442 0.115544i
\(585\) 27.0480 + 4.22642i 1.11830 + 0.174741i
\(586\) −5.14236 + 48.9263i −0.212429 + 2.02113i
\(587\) −5.38345 7.40968i −0.222199 0.305830i 0.683335 0.730105i \(-0.260529\pi\)
−0.905533 + 0.424275i \(0.860529\pi\)
\(588\) −0.0329611 0.275627i −0.00135929 0.0113667i
\(589\) −2.15753 1.56754i −0.0888994 0.0645892i
\(590\) −31.2689 11.9286i −1.28732 0.491091i
\(591\) 0.181071 + 1.72278i 0.00744828 + 0.0708656i
\(592\) 7.33991 6.60889i 0.301669 0.271624i
\(593\) −5.02610 + 2.90182i −0.206397 + 0.119164i −0.599636 0.800273i \(-0.704688\pi\)
0.393239 + 0.919436i \(0.371355\pi\)
\(594\) −3.30272 + 10.1647i −0.135512 + 0.417063i
\(595\) 7.32309 + 9.88623i 0.300217 + 0.405296i
\(596\) 0.679476 + 2.09121i 0.0278324 + 0.0856594i
\(597\) 3.09042 + 2.78263i 0.126483 + 0.113886i
\(598\) −13.5081 30.3398i −0.552389 1.24069i
\(599\) −19.9061 + 34.4783i −0.813339 + 1.40874i 0.0971751 + 0.995267i \(0.469019\pi\)
−0.910514 + 0.413478i \(0.864314\pi\)
\(600\) 2.75978 0.909398i 0.112667 0.0371260i
\(601\) −28.7332 −1.17205 −0.586025 0.810293i \(-0.699308\pi\)
−0.586025 + 0.810293i \(0.699308\pi\)
\(602\) −2.65254 16.0059i −0.108109 0.652350i
\(603\) −6.84122 + 2.22285i −0.278596 + 0.0905213i
\(604\) −2.10676 + 2.33980i −0.0857229 + 0.0952049i
\(605\) −20.8972 40.8034i −0.849593 1.65889i
\(606\) −3.67146 4.07757i −0.149143 0.165640i
\(607\) 20.8424 12.0334i 0.845966 0.488419i −0.0133215 0.999911i \(-0.504240\pi\)
0.859288 + 0.511492i \(0.170907\pi\)
\(608\) −1.19466 0.388168i −0.0484498 0.0157423i
\(609\) 0.804229 0.315331i 0.0325890 0.0127779i
\(610\) −20.2170 13.0695i −0.818564 0.529168i
\(611\) −5.25852 + 50.0315i −0.212737 + 2.02406i
\(612\) −1.11880 + 0.117591i −0.0452248 + 0.00475332i
\(613\) −47.9217 + 5.03677i −1.93554 + 0.203433i −0.991851 0.127403i \(-0.959336\pi\)
−0.943688 + 0.330836i \(0.892669\pi\)
\(614\) −2.22093 + 21.1307i −0.0896294 + 0.852766i
\(615\) −0.385780 + 0.0210214i −0.0155561 + 0.000847665i
\(616\) 37.1125 14.5515i 1.49530 0.586295i
\(617\) 10.7299 + 3.48636i 0.431970 + 0.140356i 0.516928 0.856029i \(-0.327076\pi\)
−0.0849578 + 0.996385i \(0.527076\pi\)
\(618\) 0.726378 0.419374i 0.0292192 0.0168697i
\(619\) −7.15393 7.94525i −0.287541 0.319346i 0.582018 0.813176i \(-0.302263\pi\)
−0.869559 + 0.493830i \(0.835597\pi\)
\(620\) −0.886994 + 0.142375i −0.0356225 + 0.00571792i
\(621\) −4.67541 + 5.19257i −0.187618 + 0.208371i
\(622\) 35.2376 11.4494i 1.41290 0.459079i
\(623\) −2.19717 13.2581i −0.0880278 0.531175i
\(624\) −3.88871 −0.155673
\(625\) 2.81969 + 24.8405i 0.112787 + 0.993619i
\(626\) −3.38913 + 5.87014i −0.135457 + 0.234618i
\(627\) 0.600934 + 1.34972i 0.0239990 + 0.0539026i
\(628\) −0.278956 0.251174i −0.0111316 0.0100229i
\(629\) −1.46491 4.50852i −0.0584096 0.179766i
\(630\) 14.9800 21.0234i 0.596816 0.837592i
\(631\) −0.869142 + 2.67494i −0.0346000 + 0.106488i −0.966865 0.255288i \(-0.917830\pi\)
0.932265 + 0.361776i \(0.117830\pi\)
\(632\) 3.30929 1.91062i 0.131636 0.0760003i
\(633\) 3.05258 2.74855i 0.121329 0.109245i
\(634\) 2.87238 + 27.3289i 0.114077 + 1.08537i
\(635\) −15.4198 23.6368i −0.611916 0.937997i
\(636\) 0.343725 + 0.249731i 0.0136296 + 0.00990248i
\(637\) 26.6776 + 11.4233i 1.05700 + 0.452609i
\(638\) −7.35163 10.1186i −0.291054 0.400601i
\(639\) 2.88598 27.4583i 0.114168 1.08623i
\(640\) 25.1063 12.8580i 0.992413 0.508259i
\(641\) −1.96530 18.6986i −0.0776246 0.738549i −0.962235 0.272219i \(-0.912243\pi\)
0.884611 0.466330i \(-0.154424\pi\)
\(642\) 0.578109 + 2.71979i 0.0228161 + 0.107341i
\(643\) 11.4582i 0.451866i 0.974143 + 0.225933i \(0.0725430\pi\)
−0.974143 + 0.225933i \(0.927457\pi\)
\(644\) −2.62490 0.118751i −0.103436 0.00467944i
\(645\) −1.09069 + 1.68718i −0.0429459 + 0.0664325i
\(646\) −2.50006 + 2.77659i −0.0983634 + 0.109244i
\(647\) −4.26796 + 20.0792i −0.167791 + 0.789393i 0.811084 + 0.584930i \(0.198878\pi\)
−0.978874 + 0.204463i \(0.934455\pi\)
\(648\) −9.36866 21.0424i −0.368036 0.826622i
\(649\) 28.4265 + 49.2361i 1.11584 + 1.93269i
\(650\) 6.24344 29.9850i 0.244888 1.17611i
\(651\) −0.881904 + 0.894607i −0.0345645 + 0.0350624i
\(652\) −1.31155 + 1.80519i −0.0513641 + 0.0706966i
\(653\) −14.2614 12.8411i −0.558093 0.502510i 0.341120 0.940020i \(-0.389194\pi\)
−0.899213 + 0.437510i \(0.855860\pi\)
\(654\) −5.10879 1.08591i −0.199769 0.0424623i
\(655\) −1.17419 + 7.51454i −0.0458795 + 0.293618i
\(656\) −3.38252 + 0.718977i −0.132065 + 0.0280713i
\(657\) 3.08863i 0.120499i
\(658\) 39.9678 + 25.5509i 1.55811 + 0.996079i
\(659\) −5.15208 + 3.74321i −0.200697 + 0.145815i −0.683594 0.729862i \(-0.739584\pi\)
0.482898 + 0.875677i \(0.339584\pi\)
\(660\) 0.465003 + 0.177391i 0.0181002 + 0.00690493i
\(661\) 28.2417 12.5740i 1.09847 0.489072i 0.224218 0.974539i \(-0.428017\pi\)
0.874255 + 0.485467i \(0.161350\pi\)
\(662\) −31.5469 + 3.31571i −1.22610 + 0.128869i
\(663\) −0.759153 + 1.70508i −0.0294830 + 0.0662200i
\(664\) 27.8194 + 20.2120i 1.07960 + 0.784378i
\(665\) −0.817925 7.14700i −0.0317178 0.277149i
\(666\) −8.04700 + 5.84649i −0.311815 + 0.226547i
\(667\) −1.70006 7.99814i −0.0658265 0.309689i
\(668\) 0.714397 + 0.412458i 0.0276409 + 0.0159585i
\(669\) −2.23423 2.48136i −0.0863802 0.0959349i
\(670\) 2.09905 + 7.76918i 0.0810934 + 0.300149i
\(671\) 12.6375 + 38.8943i 0.487866 + 1.50150i
\(672\) −0.264850 + 0.529117i −0.0102168 + 0.0204111i
\(673\) −7.82867 + 10.7752i −0.301773 + 0.415355i −0.932794 0.360411i \(-0.882636\pi\)
0.631021 + 0.775766i \(0.282636\pi\)
\(674\) −3.79217 6.56823i −0.146069 0.252999i
\(675\) −6.29744 + 1.36593i −0.242388 + 0.0525746i
\(676\) −0.383526 + 0.664286i −0.0147510 + 0.0255495i
\(677\) −38.3347 4.02914i −1.47332 0.154852i −0.666437 0.745561i \(-0.732182\pi\)
−0.806885 + 0.590709i \(0.798848\pi\)
\(678\) 1.79002 0.581611i 0.0687451 0.0223366i
\(679\) 21.1382 13.9432i 0.811211 0.535092i
\(680\) −0.679203 12.4646i −0.0260463 0.477994i
\(681\) 2.39903 0.509930i 0.0919310 0.0195405i
\(682\) 15.7517 + 9.09422i 0.603162 + 0.348236i
\(683\) 21.1741 19.0652i 0.810203 0.729510i −0.155870 0.987778i \(-0.549818\pi\)
0.966074 + 0.258267i \(0.0831515\pi\)
\(684\) 0.600903 + 0.267539i 0.0229761 + 0.0102296i
\(685\) 7.83669 29.4918i 0.299425 1.12682i
\(686\) 20.8921 17.6734i 0.797665 0.674774i
\(687\) −0.594067 0.817663i −0.0226651 0.0311958i
\(688\) −7.31393 + 16.4274i −0.278841 + 0.626287i
\(689\) −40.5773 + 18.0662i −1.54587 + 0.688266i
\(690\) 2.74776 + 2.73636i 0.104605 + 0.104172i
\(691\) 2.06003 + 0.917186i 0.0783674 + 0.0348914i 0.445546 0.895259i \(-0.353010\pi\)
−0.367179 + 0.930150i \(0.619676\pi\)
\(692\) −4.36254 1.41748i −0.165839 0.0538844i
\(693\) −42.2765 + 11.6526i −1.60595 + 0.442645i
\(694\) 2.75357 8.47461i 0.104524 0.321692i
\(695\) −12.9451 + 8.44491i −0.491035 + 0.320334i
\(696\) −0.857324 0.182230i −0.0324968 0.00690741i
\(697\) −0.345084 + 1.62349i −0.0130710 + 0.0614942i
\(698\) 7.18981 + 0.755679i 0.272138 + 0.0286029i
\(699\) −1.17328 −0.0443776
\(700\) −1.90032 1.50360i −0.0718254 0.0568308i
\(701\) −24.2781 −0.916972 −0.458486 0.888702i \(-0.651608\pi\)
−0.458486 + 0.888702i \(0.651608\pi\)
\(702\) 7.85130 + 0.825205i 0.296328 + 0.0311453i
\(703\) −0.576292 + 2.71124i −0.0217353 + 0.102256i
\(704\) −39.1942 8.33099i −1.47719 0.313986i
\(705\) −1.53211 5.67076i −0.0577024 0.213573i
\(706\) 10.7100 32.9621i 0.403078 1.24055i
\(707\) 11.4324 43.9203i 0.429961 1.65179i
\(708\) −0.382032 0.124130i −0.0143576 0.00466508i
\(709\) 1.40955 + 0.627572i 0.0529367 + 0.0235689i 0.433034 0.901377i \(-0.357443\pi\)
−0.380098 + 0.924946i \(0.624110\pi\)
\(710\) −30.5188 4.76874i −1.14535 0.178968i
\(711\) −3.84026 + 1.70979i −0.144021 + 0.0641222i
\(712\) −5.54608 + 12.4567i −0.207848 + 0.466834i
\(713\) 6.98931 + 9.61996i 0.261752 + 0.360270i
\(714\) 1.11733 + 1.35979i 0.0418151 + 0.0508890i
\(715\) −40.3672 + 32.8278i −1.50965 + 1.22769i
\(716\) −1.09651 0.488196i −0.0409784 0.0182448i
\(717\) 1.80657 1.62664i 0.0674675 0.0607480i
\(718\) −31.4563 18.1613i −1.17394 0.677773i
\(719\) −9.05405 + 1.92450i −0.337659 + 0.0717717i −0.373621 0.927582i \(-0.621884\pi\)
0.0359617 + 0.999353i \(0.488551\pi\)
\(720\) −26.6896 + 10.3088i −0.994661 + 0.384187i
\(721\) 6.20375 + 3.10529i 0.231040 + 0.115647i
\(722\) −24.6219 + 8.00014i −0.916332 + 0.297734i
\(723\) 4.94597 + 0.519843i 0.183943 + 0.0193332i
\(724\) −1.80865 + 3.13267i −0.0672178 + 0.116425i
\(725\) 3.03851 6.90163i 0.112848 0.256320i
\(726\) −3.27896 5.67933i −0.121694 0.210780i
\(727\) −10.0334 + 13.8097i −0.372117 + 0.512174i −0.953475 0.301473i \(-0.902522\pi\)
0.581358 + 0.813648i \(0.302522\pi\)
\(728\) −16.2131 24.5793i −0.600896 0.910971i
\(729\) 7.57155 + 23.3028i 0.280428 + 0.863068i
\(730\) 3.45115 + 0.173680i 0.127733 + 0.00642818i
\(731\) 5.77509 + 6.41388i 0.213599 + 0.237226i
\(732\) −0.250236 0.144474i −0.00924898 0.00533990i
\(733\) 5.31837 + 25.0210i 0.196438 + 0.924170i 0.960339 + 0.278836i \(0.0899486\pi\)
−0.763900 + 0.645334i \(0.776718\pi\)
\(734\) −15.9236 + 11.5692i −0.587750 + 0.427025i
\(735\) −3.38636 0.121900i −0.124908 0.00449634i
\(736\) 4.53119 + 3.29210i 0.167022 + 0.121348i
\(737\) 5.56064 12.4894i 0.204829 0.460053i
\(738\) 3.46345 0.364023i 0.127491 0.0133999i
\(739\) 8.12133 3.61585i 0.298748 0.133011i −0.251889 0.967756i \(-0.581052\pi\)
0.550637 + 0.834745i \(0.314385\pi\)
\(740\) 0.510157 + 0.782012i 0.0187537 + 0.0287473i
\(741\) 0.882896 0.641462i 0.0324340 0.0235647i
\(742\) −1.89287 + 41.8405i −0.0694894 + 1.53601i
\(743\) 10.8215i 0.397001i −0.980101 0.198500i \(-0.936393\pi\)
0.980101 0.198500i \(-0.0636071\pi\)
\(744\) 1.24674 0.265003i 0.0457077 0.00971548i
\(745\) 26.5019 4.25394i 0.970955 0.155852i
\(746\) 15.7955 + 3.35744i 0.578314 + 0.122924i
\(747\) −28.1119 25.3121i −1.02856 0.926121i
\(748\) 1.25673 1.72974i 0.0459505 0.0632454i
\(749\) −16.1459 + 16.3784i −0.589957 + 0.598455i
\(750\) 0.581451 + 3.52869i 0.0212316 + 0.128850i
\(751\) −1.41194 2.44556i −0.0515226 0.0892397i 0.839114 0.543956i \(-0.183074\pi\)
−0.890636 + 0.454716i \(0.849741\pi\)
\(752\) −21.3848 48.0311i −0.779825 1.75152i
\(753\) 1.30343 6.13217i 0.0474997 0.223469i
\(754\) −6.18179 + 6.86557i −0.225127 + 0.250029i
\(755\) 24.2492 + 29.8184i 0.882518 + 1.08520i
\(756\) 0.336427 0.526252i 0.0122357 0.0191396i
\(757\) 8.68622i 0.315706i 0.987463 + 0.157853i \(0.0504572\pi\)
−0.987463 + 0.157853i \(0.949543\pi\)
\(758\) 6.08666 + 28.6355i 0.221077 + 1.04009i
\(759\) −0.688597 6.55156i −0.0249945 0.237807i
\(760\) −3.30011 + 6.51023i −0.119708 + 0.236151i
\(761\) 0.824911 7.84850i 0.0299030 0.284508i −0.969344 0.245708i \(-0.920980\pi\)
0.999247 0.0388004i \(-0.0123536\pi\)
\(762\) −2.37298 3.26612i −0.0859639 0.118319i
\(763\) −15.7696 40.2192i −0.570897 1.45603i
\(764\) −2.26094 1.64267i −0.0817979 0.0594297i
\(765\) −0.690214 + 13.7151i −0.0249547 + 0.495869i
\(766\) 1.60083 + 15.2309i 0.0578405 + 0.550315i
\(767\) 31.2079 28.0998i 1.12685 1.01462i
\(768\) 0.817528 0.472000i 0.0295000 0.0170318i
\(769\) 12.2384 37.6658i 0.441327 1.35826i −0.445136 0.895463i \(-0.646845\pi\)
0.886462 0.462800i \(-0.153155\pi\)
\(770\) 10.6430 + 47.8938i 0.383546 + 1.72597i
\(771\) −1.62806 5.01066i −0.0586333 0.180455i
\(772\) 0.467480 + 0.420920i 0.0168250 + 0.0151493i
\(773\) 5.79731 + 13.0210i 0.208515 + 0.468332i 0.987282 0.158982i \(-0.0508211\pi\)
−0.778767 + 0.627314i \(0.784154\pi\)
\(774\) 9.05454 15.6829i 0.325459 0.563711i
\(775\) 0.0455542 + 10.9660i 0.00163635 + 0.393912i
\(776\) −25.6932 −0.922331
\(777\) 1.22225 + 0.459177i 0.0438480 + 0.0164729i
\(778\) −9.47741 + 3.07940i −0.339782 + 0.110402i
\(779\) 0.649371 0.721200i 0.0232661 0.0258397i
\(780\) 0.0567539 0.363211i 0.00203212 0.0130050i
\(781\) 35.1118 + 38.9957i 1.25640 + 1.39537i
\(782\) 14.4273 8.32963i 0.515921 0.297867i
\(783\) 1.84857 + 0.600637i 0.0660625 + 0.0214650i
\(784\) −30.1151 + 3.60134i −1.07554 + 0.128619i
\(785\) −3.55503 + 2.89105i −0.126884 + 0.103186i
\(786\) −0.113728 + 1.08205i −0.00405653 + 0.0385953i
\(787\) 52.2040 5.48686i 1.86087 0.195585i 0.893520 0.449024i \(-0.148228\pi\)
0.967351 + 0.253439i \(0.0815617\pi\)
\(788\) −1.45772 + 0.153212i −0.0519291 + 0.00545797i
\(789\) −0.0995820 + 0.947459i −0.00354521 + 0.0337304i
\(790\) 1.69453 + 4.38714i 0.0602886 + 0.156087i
\(791\) 12.1681 + 9.71029i 0.432648 + 0.345258i
\(792\) 42.3169 + 13.7496i 1.50366 + 0.488570i
\(793\) 26.1606 15.1039i 0.928991 0.536353i
\(794\) −13.4088 14.8920i −0.475860 0.528496i
\(795\) 3.65969 3.67492i 0.129796 0.130336i
\(796\) −2.35451 + 2.61495i −0.0834533 + 0.0926843i
\(797\) 10.3756 3.37124i 0.367523 0.119415i −0.119432 0.992842i \(-0.538107\pi\)
0.486955 + 0.873427i \(0.338107\pi\)
\(798\) −0.168244 1.01521i −0.00595577 0.0359381i
\(799\) −25.2350 −0.892749
\(800\) 1.61655 + 4.90578i 0.0571535 + 0.173446i
\(801\) 7.50013 12.9906i 0.265004 0.459001i
\(802\) 3.25896 + 7.31975i 0.115078 + 0.258469i
\(803\) −4.36238 3.92791i −0.153945 0.138613i
\(804\) 0.0298492 + 0.0918665i 0.00105270 + 0.00323988i
\(805\) −6.37897 + 31.4342i −0.224829 + 1.10791i
\(806\) 4.15161 12.7773i 0.146234 0.450062i
\(807\) −3.66314 + 2.11491i −0.128948 + 0.0744485i
\(808\) −34.2202 + 30.8120i −1.20386 + 1.08396i
\(809\) 1.03588 + 9.85574i 0.0364196 + 0.346510i 0.997524 + 0.0703247i \(0.0224035\pi\)
−0.961105 + 0.276185i \(0.910930\pi\)
\(810\) 27.3677 7.39411i 0.961603 0.259803i
\(811\) −6.80591 4.94478i −0.238988 0.173635i 0.461844 0.886961i \(-0.347188\pi\)
−0.700832 + 0.713326i \(0.747188\pi\)
\(812\) 0.266816 + 0.680494i 0.00936339 + 0.0238807i
\(813\) −2.88637 3.97275i −0.101230 0.139331i
\(814\) 1.97604 18.8007i 0.0692601 0.658965i
\(815\) 19.3001 + 19.2201i 0.676052 + 0.673250i
\(816\) −0.203898 1.93996i −0.00713787 0.0679123i
\(817\) −1.04921 4.93615i −0.0367072 0.172694i
\(818\) 7.22290i 0.252543i
\(819\) 14.9117 + 28.7556i 0.521055 + 1.00480i
\(820\) −0.0177872 0.326425i −0.000621154 0.0113993i
\(821\) −23.7986 + 26.4311i −0.830578 + 0.922450i −0.997986 0.0634374i \(-0.979794\pi\)
0.167408 + 0.985888i \(0.446460\pi\)
\(822\) 0.907584 4.26985i 0.0316556 0.148928i
\(823\) −15.2354 34.2193i −0.531073 1.19281i −0.957539 0.288305i \(-0.906908\pi\)
0.426466 0.904504i \(-0.359758\pi\)
\(824\) −3.51952 6.09598i −0.122608 0.212364i
\(825\) 3.01577 5.27395i 0.104996 0.183615i
\(826\) −10.5221 38.1750i −0.366111 1.32828i
\(827\) 13.8903 19.1183i 0.483012 0.664808i −0.496069 0.868283i \(-0.665224\pi\)
0.979080 + 0.203475i \(0.0652236\pi\)
\(828\) −2.17954 1.96246i −0.0757441 0.0682003i
\(829\) −26.6170 5.65763i −0.924448 0.196497i −0.278991 0.960294i \(-0.590000\pi\)
−0.645457 + 0.763796i \(0.723333\pi\)
\(830\) −29.8638 + 29.9881i −1.03659 + 1.04090i
\(831\) −1.81672 + 0.386157i −0.0630215 + 0.0133956i
\(832\) 29.5976i 1.02611i
\(833\) −4.29997 + 13.9076i −0.148985 + 0.481870i
\(834\) −1.78875 + 1.29960i −0.0619393 + 0.0450015i
\(835\) 6.32083 7.83881i 0.218741 0.271273i
\(836\) −1.14206 + 0.508477i −0.0394989 + 0.0175861i
\(837\) −2.81109 + 0.295458i −0.0971655 + 0.0102125i
\(838\) 10.8625 24.3976i 0.375240 0.842802i
\(839\) −12.5349 9.10712i −0.432752 0.314413i 0.349996 0.936751i \(-0.386183\pi\)
−0.782748 + 0.622338i \(0.786183\pi\)
\(840\) 2.80003 + 1.99513i 0.0966103 + 0.0688385i
\(841\) 21.6213 15.7088i 0.745562 0.541683i
\(842\) −5.41843 25.4917i −0.186731 0.878502i
\(843\) −1.61143 0.930358i −0.0555005 0.0320432i
\(844\) 2.32567 + 2.58292i 0.0800529 + 0.0889078i
\(845\) 7.28895 + 5.87745i 0.250748 + 0.202191i
\(846\) 16.3619 + 50.3568i 0.562534 + 1.73130i
\(847\) 24.2794 48.5053i 0.834249 1.66666i
\(848\) 27.2857 37.5555i 0.936994 1.28966i
\(849\) 1.68739 + 2.92264i 0.0579110 + 0.100305i
\(850\) 15.2860 + 1.54245i 0.524305 + 0.0529056i
\(851\) 6.17946 10.7031i 0.211829 0.366899i
\(852\) −0.368720 0.0387540i −0.0126321 0.00132769i
\(853\) −20.6326 + 6.70395i −0.706448 + 0.229539i −0.640138 0.768260i \(-0.721123\pi\)
−0.0663103 + 0.997799i \(0.521123\pi\)
\(854\) −1.69411 28.4339i −0.0579714 0.972988i
\(855\) 4.35913 6.74309i 0.149079 0.230609i
\(856\) 22.8253 4.85166i 0.780152 0.165826i
\(857\) −43.4273 25.0728i −1.48345 0.856470i −0.483626 0.875275i \(-0.660680\pi\)
−0.999823 + 0.0188051i \(0.994014\pi\)
\(858\) −5.53124 + 4.98035i −0.188833 + 0.170026i
\(859\) 12.5897 + 5.60531i 0.429556 + 0.191251i 0.610114 0.792314i \(-0.291124\pi\)
−0.180558 + 0.983564i \(0.557790\pi\)
\(860\) −1.42760 0.922881i −0.0486806 0.0314700i
\(861\) −0.290219 0.353197i −0.00989064 0.0120369i
\(862\) −1.76397 2.42789i −0.0600810 0.0826944i
\(863\) 8.18348 18.3804i 0.278569 0.625676i −0.719026 0.694983i \(-0.755412\pi\)
0.997595 + 0.0693067i \(0.0220787\pi\)
\(864\) −1.21627 + 0.541517i −0.0413783 + 0.0184228i
\(865\) −25.3171 + 49.9439i −0.860809 + 1.69814i
\(866\) 44.8029 + 19.9475i 1.52246 + 0.677845i
\(867\) 2.60973 + 0.847952i 0.0886310 + 0.0287979i
\(868\) −0.756967 0.746218i −0.0256931 0.0253283i
\(869\) 2.46886 7.59837i 0.0837504 0.257757i
\(870\) 0.384490 1.00788i 0.0130354 0.0341705i
\(871\) −9.87766 2.09956i −0.334692 0.0711409i
\(872\) −9.11325 + 42.8745i −0.308614 + 1.45191i
\(873\) 28.1098 + 2.95446i 0.951374 + 0.0999934i
\(874\) −9.74074 −0.329485
\(875\) −21.7157 + 20.0855i −0.734124 + 0.679015i
\(876\) 0.0414753 0.00140132
\(877\) 22.8078 + 2.39720i 0.770165 + 0.0809476i 0.481457 0.876470i \(-0.340108\pi\)
0.288708 + 0.957417i \(0.406774\pi\)
\(878\) 3.64871 17.1658i 0.123138 0.579318i
\(879\) 7.05048 + 1.49863i 0.237807 + 0.0505474i
\(880\) 19.3818 50.8064i 0.653359 1.71268i
\(881\) 8.66279 26.6613i 0.291857 0.898243i −0.692402 0.721512i \(-0.743448\pi\)
0.984259 0.176731i \(-0.0565524\pi\)
\(882\) 30.5409 0.436797i 1.02836 0.0147077i
\(883\) −8.92235 2.89905i −0.300261 0.0975607i 0.155012 0.987913i \(-0.450458\pi\)
−0.455273 + 0.890352i \(0.650458\pi\)
\(884\) −1.44275 0.642353i −0.0485249 0.0216047i
\(885\) −2.21704 + 4.37363i −0.0745251 + 0.147018i
\(886\) 35.2783 15.7069i 1.18520 0.527683i
\(887\) −14.3449 + 32.2191i −0.481653 + 1.08181i 0.495371 + 0.868682i \(0.335032\pi\)
−0.977024 + 0.213129i \(0.931634\pi\)
\(888\) −0.778673 1.07175i −0.0261306 0.0359656i
\(889\) 11.7436 31.2593i 0.393866 1.04840i
\(890\) −14.0936 9.11092i −0.472418 0.305399i
\(891\) −43.9952 19.5879i −1.47389 0.656220i
\(892\) 2.09959 1.89048i 0.0702995 0.0632979i
\(893\) 12.7782 + 7.37750i 0.427606 + 0.246878i
\(894\) 3.75575 0.798309i 0.125611 0.0266994i
\(895\) −7.95440 + 12.3046i −0.265886 + 0.411296i
\(896\) 29.8453 + 14.9391i 0.997060 + 0.499080i
\(897\) −4.62781 + 1.50367i −0.154518 + 0.0502059i
\(898\) 19.8208 + 2.08325i 0.661429 + 0.0695190i
\(899\) 1.65389 2.86462i 0.0551603 0.0955404i
\(900\) −0.573337 2.64330i −0.0191112 0.0881099i
\(901\) −11.1403 19.2955i −0.371136 0.642827i
\(902\) −3.89043 + 5.35472i −0.129537 + 0.178293i
\(903\) −2.37290 + 0.141379i −0.0789651 + 0.00470480i
\(904\) −4.88106 15.0223i −0.162341 0.499636i
\(905\) 34.3735 + 27.7171i 1.14261 + 0.921348i
\(906\) 3.67888 + 4.08581i 0.122223 + 0.135742i
\(907\) −25.8405 14.9190i −0.858021 0.495379i 0.00532811 0.999986i \(-0.498304\pi\)
−0.863349 + 0.504607i \(0.831637\pi\)
\(908\) 0.431474 + 2.02993i 0.0143190 + 0.0673655i
\(909\) 40.9820 29.7751i 1.35929 0.987579i
\(910\) 32.9692 15.0449i 1.09292 0.498732i
\(911\) 4.62700 + 3.36171i 0.153299 + 0.111379i 0.661791 0.749688i \(-0.269797\pi\)
−0.508491 + 0.861067i \(0.669797\pi\)
\(912\) −0.463905 + 1.04195i −0.0153614 + 0.0345023i
\(913\) 71.5016 7.51512i 2.36636 0.248714i
\(914\) −26.1778 + 11.6551i −0.865885 + 0.385517i
\(915\) −2.21403 + 2.74574i −0.0731936 + 0.0907714i
\(916\) 0.691861 0.502666i 0.0228597 0.0166086i
\(917\) −7.98894 + 4.14279i −0.263818 + 0.136807i
\(918\) 3.96005i 0.130701i
\(919\) −35.6448 + 7.57654i −1.17581 + 0.249927i −0.754074 0.656789i \(-0.771914\pi\)
−0.421741 + 0.906716i \(0.638581\pi\)
\(920\) 22.9644 23.0600i 0.757114 0.760265i
\(921\) 3.04502 + 0.647240i 0.100337 + 0.0213273i
\(922\) −35.6319 32.0831i −1.17347 1.05660i
\(923\) 22.7824 31.3573i 0.749892 1.03214i
\(924\) 0.156475 + 0.567705i 0.00514766 + 0.0186761i
\(925\) 10.3930 4.67909i 0.341720 0.153848i
\(926\) 8.44639 + 14.6296i 0.277566 + 0.480758i
\(927\) 3.14958 + 7.07407i 0.103446 + 0.232343i
\(928\) 0.323932 1.52398i 0.0106336 0.0500271i
\(929\) 10.9770 12.1912i 0.360145 0.399981i −0.535657 0.844436i \(-0.679936\pi\)
0.895801 + 0.444455i \(0.146603\pi\)
\(930\) 0.0853539 + 1.56639i 0.00279887 + 0.0513641i
\(931\) 6.24329 5.78527i 0.204615 0.189605i
\(932\) 0.992766i 0.0325191i
\(933\) −1.12867 5.30995i −0.0369509 0.173840i
\(934\) 3.60806 + 34.3284i 0.118059 + 1.12326i
\(935\) −18.4934 18.4167i −0.604798 0.602291i
\(936\) 3.43542 32.6859i 0.112290 1.06837i
\(937\) 1.74631 + 2.40359i 0.0570494 + 0.0785218i 0.836588 0.547832i \(-0.184547\pi\)
−0.779539 + 0.626354i \(0.784547\pi\)
\(938\) −5.93945 + 7.44281i −0.193930 + 0.243016i
\(939\) 0.803456 + 0.583745i 0.0262198 + 0.0190498i
\(940\) 4.79828 1.29638i 0.156503 0.0422833i
\(941\) 5.09338 + 48.4603i 0.166040 + 1.57976i 0.687307 + 0.726368i \(0.258793\pi\)
−0.521267 + 0.853394i \(0.674540\pi\)
\(942\) −0.487121 + 0.438605i −0.0158712 + 0.0142905i
\(943\) −3.74740 + 2.16356i −0.122032 + 0.0704552i
\(944\) −13.5624 + 41.7409i −0.441419 + 1.35855i
\(945\) −5.71294 5.04928i −0.185842 0.164253i
\(946\) 10.6356 + 32.7331i 0.345794 + 1.06424i
\(947\) 21.1250 + 19.0210i 0.686470 + 0.618101i 0.936720 0.350081i \(-0.113846\pi\)
−0.250249 + 0.968181i \(0.580513\pi\)
\(948\) 0.0229598 + 0.0515685i 0.000745698 + 0.00167487i
\(949\) −2.16800 + 3.75508i −0.0703762 + 0.121895i
\(950\) −7.28941 5.24994i −0.236500 0.170331i
\(951\) 4.02619 0.130558
\(952\) 11.4118 9.37699i 0.369859 0.303910i
\(953\) −9.66067 + 3.13894i −0.312940 + 0.101680i −0.461276 0.887257i \(-0.652608\pi\)
0.148336 + 0.988937i \(0.452608\pi\)
\(954\) −31.2814 + 34.7415i −1.01277 + 1.12480i
\(955\) −24.0725 + 24.1727i −0.778968 + 0.782211i
\(956\) 1.37637 + 1.52862i 0.0445151 + 0.0494390i
\(957\) −1.58702 + 0.916265i −0.0513010 + 0.0296186i
\(958\) 52.8776 + 17.1810i 1.70840 + 0.555092i
\(959\) 33.6146 13.1800i 1.08547 0.425604i
\(960\) −1.24520 3.22382i −0.0401886 0.104048i
\(961\) 2.73757 26.0463i 0.0883089 0.840203i
\(962\) −13.8872 + 1.45960i −0.447740 + 0.0470593i
\(963\) −25.5301 + 2.68332i −0.822695 + 0.0864688i
\(964\) −0.439862 + 4.18501i −0.0141670 + 0.134790i
\(965\) 5.95757 4.84487i 0.191781 0.155962i
\(966\) −0.685353 + 4.53688i −0.0220509 + 0.145972i
\(967\) −6.99426 2.27257i −0.224920 0.0730810i 0.194389 0.980925i \(-0.437728\pi\)
−0.419309 + 0.907844i \(0.637728\pi\)
\(968\) −47.6627 + 27.5180i −1.53194 + 0.884464i
\(969\) 0.366299 + 0.406817i 0.0117672 + 0.0130688i
\(970\) 4.88190 31.2430i 0.156748 1.00315i
\(971\) 16.6864 18.5322i 0.535493 0.594725i −0.413311 0.910590i \(-0.635628\pi\)
0.948804 + 0.315865i \(0.102295\pi\)
\(972\) 0.997175 0.324002i 0.0319844 0.0103924i
\(973\) −17.1197 6.43156i −0.548832 0.206186i
\(974\) 13.2927 0.425925
\(975\) −4.27361 1.36898i −0.136865 0.0438425i
\(976\) −15.7852 + 27.3408i −0.505273 + 0.875159i
\(977\) −2.47781 5.56524i −0.0792720 0.178048i 0.869561 0.493825i \(-0.164402\pi\)
−0.948833 + 0.315777i \(0.897735\pi\)
\(978\) 2.89560 + 2.60721i 0.0925910 + 0.0833693i
\(979\) 8.80979 + 27.1137i 0.281562 + 0.866559i
\(980\) 0.103145 2.86535i 0.00329484 0.0915302i
\(981\) 14.9006 45.8593i 0.475739 1.46417i
\(982\) −23.5052 + 13.5708i −0.750082 + 0.433060i
\(983\) −3.59748 + 3.23919i −0.114742 + 0.103314i −0.724505 0.689270i \(-0.757931\pi\)
0.609763 + 0.792584i \(0.291265\pi\)
\(984\) 0.0484830 + 0.461285i 0.00154558 + 0.0147052i
\(985\) −0.899302 + 17.8698i −0.0286541 + 0.569379i
\(986\) −3.74916 2.72392i −0.119398 0.0867474i
\(987\) 4.33524 5.43254i 0.137992 0.172920i
\(988\) 0.542769 + 0.747058i 0.0172678 + 0.0237671i
\(989\) −2.35199 + 22.3777i −0.0747889 + 0.711569i
\(990\) −24.7601 + 48.8449i −0.786927 + 1.55239i
\(991\) −3.84322 36.5658i −0.122084 1.16155i −0.868367 0.495922i \(-0.834830\pi\)
0.746283 0.665629i \(-0.231837\pi\)
\(992\) 0.471069 + 2.21621i 0.0149565 + 0.0703646i
\(993\) 4.64760i 0.147487i
\(994\) −16.8251 32.4454i −0.533659 1.02911i
\(995\) 27.1008 + 33.3249i 0.859153 + 1.05647i
\(996\) −0.339900 + 0.377498i −0.0107702 + 0.0119615i
\(997\) 5.52813 26.0078i 0.175078 0.823675i −0.799683 0.600422i \(-0.794999\pi\)
0.974761 0.223253i \(-0.0716675\pi\)
\(998\) −13.7873 30.9669i −0.436431 0.980239i
\(999\) 1.46891 + 2.54423i 0.0464743 + 0.0804958i
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 175.2.t.a.109.13 yes 144
5.2 odd 4 875.2.q.b.326.11 288
5.3 odd 4 875.2.q.b.326.26 288
5.4 even 2 875.2.u.a.424.6 144
7.2 even 3 inner 175.2.t.a.9.6 144
25.2 odd 20 875.2.q.b.676.26 288
25.11 even 5 875.2.u.a.74.13 144
25.14 even 10 inner 175.2.t.a.39.6 yes 144
25.23 odd 20 875.2.q.b.676.11 288
35.2 odd 12 875.2.q.b.576.26 288
35.9 even 6 875.2.u.a.674.13 144
35.23 odd 12 875.2.q.b.576.11 288
175.2 odd 60 875.2.q.b.51.11 288
175.23 odd 60 875.2.q.b.51.26 288
175.86 even 15 875.2.u.a.324.6 144
175.114 even 30 inner 175.2.t.a.114.13 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.t.a.9.6 144 7.2 even 3 inner
175.2.t.a.39.6 yes 144 25.14 even 10 inner
175.2.t.a.109.13 yes 144 1.1 even 1 trivial
175.2.t.a.114.13 yes 144 175.114 even 30 inner
875.2.q.b.51.11 288 175.2 odd 60
875.2.q.b.51.26 288 175.23 odd 60
875.2.q.b.326.11 288 5.2 odd 4
875.2.q.b.326.26 288 5.3 odd 4
875.2.q.b.576.11 288 35.23 odd 12
875.2.q.b.576.26 288 35.2 odd 12
875.2.q.b.676.11 288 25.23 odd 20
875.2.q.b.676.26 288 25.2 odd 20
875.2.u.a.74.13 144 25.11 even 5
875.2.u.a.324.6 144 175.86 even 15
875.2.u.a.424.6 144 5.4 even 2
875.2.u.a.674.13 144 35.9 even 6