Properties

Label 690.2.m.c.211.1
Level $690$
Weight $2$
Character 690.211
Analytic conductor $5.510$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,2,Mod(31,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.m (of order \(11\), degree \(10\), 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: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + 17043 x^{12} - 35832 x^{11} + 60906 x^{10} - 87666 x^{9} + 106197 x^{8} - 102542 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 211.1
Root \(-0.608732 - 1.33294i\) of defining polynomial
Character \(\chi\) \(=\) 690.211
Dual form 690.2.m.c.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.668052 - 4.64640i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\) \(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(-0.668052 - 4.64640i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.142315 + 0.989821i) q^{10} +(0.596110 - 1.30530i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.659144 - 4.58445i) q^{13} +(3.94900 - 2.53787i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.16545 + 2.49906i) q^{17} +(0.841254 + 0.540641i) q^{18} +(2.75889 - 3.18393i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(-1.95003 - 4.26998i) q^{21} +1.43497 q^{22} +(-2.66976 + 3.98402i) q^{23} -1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(4.44398 - 1.30487i) q^{26} +(0.654861 - 0.755750i) q^{27} +(3.94900 + 2.53787i) q^{28} +(-2.01362 - 2.32384i) q^{29} +(0.142315 + 0.989821i) q^{30} +(9.43317 + 2.76983i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.204218 - 1.42037i) q^{33} +(-1.37367 + 3.00791i) q^{34} +(1.95003 - 4.26998i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-9.64008 + 6.19530i) q^{37} +(4.04228 + 1.18692i) q^{38} +(-0.659144 - 4.58445i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(2.56811 + 1.65043i) q^{41} +(3.07404 - 3.54763i) q^{42} +(-4.11868 + 1.20935i) q^{43} +(0.596110 + 1.30530i) q^{44} +1.00000 q^{45} +(-4.73305 - 0.773476i) q^{46} +0.295107 q^{47} +(-0.415415 - 0.909632i) q^{48} +(-14.4263 + 4.23595i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(2.78180 + 1.78775i) q^{51} +(3.03305 + 3.50032i) q^{52} +(1.91236 + 13.3007i) q^{53} +(0.959493 + 0.281733i) q^{54} +(1.20718 - 0.775805i) q^{55} +(-0.668052 + 4.64640i) q^{56} +(1.75012 - 3.83222i) q^{57} +(1.27735 - 2.79701i) q^{58} +(2.09506 - 14.5715i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(8.12938 + 2.38700i) q^{61} +(1.39916 + 9.73134i) q^{62} +(-3.07404 - 3.54763i) q^{63} +(0.841254 + 0.540641i) q^{64} +(3.03305 - 3.50032i) q^{65} +(1.37685 - 0.404279i) q^{66} +(-4.93976 - 10.8166i) q^{67} -3.30673 q^{68} +(-1.43919 + 4.57479i) q^{69} +4.69418 q^{70} +(4.97324 + 10.8899i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(5.60463 - 6.46809i) q^{73} +(-9.64008 - 6.19530i) q^{74} +(0.654861 + 0.755750i) q^{75} +(0.599564 + 4.17006i) q^{76} +(-6.46318 - 1.89776i) q^{77} +(3.89634 - 2.50403i) q^{78} +(-1.95489 + 13.5966i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.434447 + 3.02165i) q^{82} +(7.86619 - 5.05530i) q^{83} +(4.50404 + 1.32250i) q^{84} +(0.470597 + 3.27307i) q^{85} +(-2.81103 - 3.24410i) q^{86} +(-2.58675 - 1.66240i) q^{87} +(-0.939708 + 1.08448i) q^{88} +(-5.33745 + 1.56722i) q^{89} +(0.415415 + 0.909632i) q^{90} -21.7415 q^{91} +(-1.26260 - 4.62664i) q^{92} +9.83141 q^{93} +(0.122592 + 0.268439i) q^{94} +(4.04228 - 1.18692i) q^{95} +(0.654861 - 0.755750i) q^{96} +(-8.67436 - 5.57468i) q^{97} +(-9.84608 - 11.3630i) q^{98} +(-0.204218 - 1.42037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.415415 + 0.909632i 0.293743 + 0.643207i
\(3\) 0.959493 0.281733i 0.553964 0.162658i
\(4\) −0.654861 + 0.755750i −0.327430 + 0.377875i
\(5\) 0.841254 + 0.540641i 0.376220 + 0.241782i
\(6\) 0.654861 + 0.755750i 0.267346 + 0.308533i
\(7\) −0.668052 4.64640i −0.252500 1.75618i −0.583096 0.812404i \(-0.698159\pi\)
0.330596 0.943772i \(-0.392750\pi\)
\(8\) −0.959493 0.281733i −0.339232 0.0996075i
\(9\) 0.841254 0.540641i 0.280418 0.180214i
\(10\) −0.142315 + 0.989821i −0.0450039 + 0.313009i
\(11\) 0.596110 1.30530i 0.179734 0.393562i −0.798225 0.602359i \(-0.794228\pi\)
0.977959 + 0.208797i \(0.0669548\pi\)
\(12\) −0.415415 + 0.909632i −0.119920 + 0.262588i
\(13\) 0.659144 4.58445i 0.182814 1.27150i −0.667257 0.744828i \(-0.732532\pi\)
0.850070 0.526669i \(-0.176559\pi\)
\(14\) 3.94900 2.53787i 1.05541 0.678274i
\(15\) 0.959493 + 0.281733i 0.247740 + 0.0727430i
\(16\) −0.142315 0.989821i −0.0355787 0.247455i
\(17\) 2.16545 + 2.49906i 0.525198 + 0.606111i 0.954925 0.296848i \(-0.0959355\pi\)
−0.429727 + 0.902959i \(0.641390\pi\)
\(18\) 0.841254 + 0.540641i 0.198285 + 0.127430i
\(19\) 2.75889 3.18393i 0.632932 0.730443i −0.345176 0.938538i \(-0.612181\pi\)
0.978109 + 0.208095i \(0.0667264\pi\)
\(20\) −0.959493 + 0.281733i −0.214549 + 0.0629973i
\(21\) −1.95003 4.26998i −0.425533 0.931786i
\(22\) 1.43497 0.305937
\(23\) −2.66976 + 3.98402i −0.556683 + 0.830725i
\(24\) −1.00000 −0.204124
\(25\) 0.415415 + 0.909632i 0.0830830 + 0.181926i
\(26\) 4.44398 1.30487i 0.871536 0.255906i
\(27\) 0.654861 0.755750i 0.126028 0.145444i
\(28\) 3.94900 + 2.53787i 0.746291 + 0.479612i
\(29\) −2.01362 2.32384i −0.373919 0.431526i 0.537336 0.843368i \(-0.319431\pi\)
−0.911255 + 0.411843i \(0.864885\pi\)
\(30\) 0.142315 + 0.989821i 0.0259830 + 0.180716i
\(31\) 9.43317 + 2.76983i 1.69425 + 0.497476i 0.979421 0.201826i \(-0.0646876\pi\)
0.714826 + 0.699302i \(0.246506\pi\)
\(32\) 0.841254 0.540641i 0.148714 0.0955727i
\(33\) 0.204218 1.42037i 0.0355498 0.247254i
\(34\) −1.37367 + 3.00791i −0.235582 + 0.515852i
\(35\) 1.95003 4.26998i 0.329616 0.721758i
\(36\) −0.142315 + 0.989821i −0.0237191 + 0.164970i
\(37\) −9.64008 + 6.19530i −1.58482 + 1.01850i −0.610871 + 0.791730i \(0.709181\pi\)
−0.973948 + 0.226772i \(0.927183\pi\)
\(38\) 4.04228 + 1.18692i 0.655745 + 0.192544i
\(39\) −0.659144 4.58445i −0.105548 0.734099i
\(40\) −0.654861 0.755750i −0.103543 0.119494i
\(41\) 2.56811 + 1.65043i 0.401072 + 0.257753i 0.725591 0.688126i \(-0.241566\pi\)
−0.324520 + 0.945879i \(0.605203\pi\)
\(42\) 3.07404 3.54763i 0.474334 0.547411i
\(43\) −4.11868 + 1.20935i −0.628092 + 0.184425i −0.580261 0.814431i \(-0.697049\pi\)
−0.0478318 + 0.998855i \(0.515231\pi\)
\(44\) 0.596110 + 1.30530i 0.0898669 + 0.196781i
\(45\) 1.00000 0.149071
\(46\) −4.73305 0.773476i −0.697850 0.114043i
\(47\) 0.295107 0.0430457 0.0215229 0.999768i \(-0.493149\pi\)
0.0215229 + 0.999768i \(0.493149\pi\)
\(48\) −0.415415 0.909632i −0.0599600 0.131294i
\(49\) −14.4263 + 4.23595i −2.06090 + 0.605136i
\(50\) −0.654861 + 0.755750i −0.0926113 + 0.106879i
\(51\) 2.78180 + 1.78775i 0.389530 + 0.250336i
\(52\) 3.03305 + 3.50032i 0.420608 + 0.485407i
\(53\) 1.91236 + 13.3007i 0.262683 + 1.82700i 0.512479 + 0.858700i \(0.328727\pi\)
−0.249796 + 0.968298i \(0.580364\pi\)
\(54\) 0.959493 + 0.281733i 0.130570 + 0.0383389i
\(55\) 1.20718 0.775805i 0.162776 0.104610i
\(56\) −0.668052 + 4.64640i −0.0892722 + 0.620902i
\(57\) 1.75012 3.83222i 0.231809 0.507590i
\(58\) 1.27735 2.79701i 0.167724 0.367265i
\(59\) 2.09506 14.5715i 0.272754 1.89705i −0.146555 0.989203i \(-0.546819\pi\)
0.419309 0.907844i \(-0.362272\pi\)
\(60\) −0.841254 + 0.540641i −0.108605 + 0.0697964i
\(61\) 8.12938 + 2.38700i 1.04086 + 0.305624i 0.757119 0.653277i \(-0.226606\pi\)
0.283741 + 0.958901i \(0.408424\pi\)
\(62\) 1.39916 + 9.73134i 0.177693 + 1.23588i
\(63\) −3.07404 3.54763i −0.387292 0.446959i
\(64\) 0.841254 + 0.540641i 0.105157 + 0.0675801i
\(65\) 3.03305 3.50032i 0.376203 0.434162i
\(66\) 1.37685 0.404279i 0.169478 0.0497633i
\(67\) −4.93976 10.8166i −0.603488 1.32145i −0.926940 0.375209i \(-0.877571\pi\)
0.323453 0.946244i \(-0.395156\pi\)
\(68\) −3.30673 −0.401000
\(69\) −1.43919 + 4.57479i −0.173258 + 0.550741i
\(70\) 4.69418 0.561062
\(71\) 4.97324 + 10.8899i 0.590215 + 1.29239i 0.935312 + 0.353823i \(0.115119\pi\)
−0.345097 + 0.938567i \(0.612154\pi\)
\(72\) −0.959493 + 0.281733i −0.113077 + 0.0332025i
\(73\) 5.60463 6.46809i 0.655972 0.757033i −0.326141 0.945321i \(-0.605749\pi\)
0.982114 + 0.188288i \(0.0602940\pi\)
\(74\) −9.64008 6.19530i −1.12064 0.720189i
\(75\) 0.654861 + 0.755750i 0.0756168 + 0.0872664i
\(76\) 0.599564 + 4.17006i 0.0687747 + 0.478338i
\(77\) −6.46318 1.89776i −0.736547 0.216270i
\(78\) 3.89634 2.50403i 0.441174 0.283525i
\(79\) −1.95489 + 13.5966i −0.219943 + 1.52974i 0.518299 + 0.855200i \(0.326566\pi\)
−0.738242 + 0.674536i \(0.764344\pi\)
\(80\) 0.415415 0.909632i 0.0464448 0.101700i
\(81\) 0.415415 0.909632i 0.0461572 0.101070i
\(82\) −0.434447 + 3.02165i −0.0479767 + 0.333685i
\(83\) 7.86619 5.05530i 0.863427 0.554891i −0.0323087 0.999478i \(-0.510286\pi\)
0.895736 + 0.444587i \(0.146650\pi\)
\(84\) 4.50404 + 1.32250i 0.491431 + 0.144297i
\(85\) 0.470597 + 3.27307i 0.0510434 + 0.355015i
\(86\) −2.81103 3.24410i −0.303121 0.349820i
\(87\) −2.58675 1.66240i −0.277329 0.178228i
\(88\) −0.939708 + 1.08448i −0.100173 + 0.115606i
\(89\) −5.33745 + 1.56722i −0.565768 + 0.166125i −0.552094 0.833782i \(-0.686171\pi\)
−0.0136745 + 0.999906i \(0.504353\pi\)
\(90\) 0.415415 + 0.909632i 0.0437886 + 0.0958836i
\(91\) −21.7415 −2.27913
\(92\) −1.26260 4.62664i −0.131635 0.482361i
\(93\) 9.83141 1.01947
\(94\) 0.122592 + 0.268439i 0.0126444 + 0.0276873i
\(95\) 4.04228 1.18692i 0.414730 0.121776i
\(96\) 0.654861 0.755750i 0.0668364 0.0771334i
\(97\) −8.67436 5.57468i −0.880748 0.566023i 0.0202745 0.999794i \(-0.493546\pi\)
−0.901023 + 0.433772i \(0.857182\pi\)
\(98\) −9.84608 11.3630i −0.994604 1.14783i
\(99\) −0.204218 1.42037i −0.0205247 0.142752i
\(100\) −0.959493 0.281733i −0.0959493 0.0281733i
\(101\) −1.92412 + 1.23656i −0.191457 + 0.123042i −0.632858 0.774268i \(-0.718118\pi\)
0.441400 + 0.897310i \(0.354482\pi\)
\(102\) −0.470597 + 3.27307i −0.0465960 + 0.324082i
\(103\) −0.0449425 + 0.0984103i −0.00442831 + 0.00969665i −0.911833 0.410561i \(-0.865333\pi\)
0.907405 + 0.420257i \(0.138060\pi\)
\(104\) −1.92403 + 4.21304i −0.188667 + 0.413123i
\(105\) 0.668052 4.64640i 0.0651952 0.453443i
\(106\) −11.3044 + 7.26487i −1.09798 + 0.705627i
\(107\) 11.6565 + 3.42266i 1.12688 + 0.330881i 0.791479 0.611196i \(-0.209311\pi\)
0.335398 + 0.942077i \(0.391129\pi\)
\(108\) 0.142315 + 0.989821i 0.0136943 + 0.0952456i
\(109\) −0.552043 0.637092i −0.0528762 0.0610223i 0.728695 0.684838i \(-0.240127\pi\)
−0.781572 + 0.623816i \(0.785582\pi\)
\(110\) 1.20718 + 0.775805i 0.115100 + 0.0739701i
\(111\) −7.50417 + 8.66027i −0.712264 + 0.821997i
\(112\) −4.50404 + 1.32250i −0.425592 + 0.124965i
\(113\) −5.19756 11.3811i −0.488945 1.07064i −0.979906 0.199459i \(-0.936082\pi\)
0.490961 0.871182i \(-0.336646\pi\)
\(114\) 4.21294 0.394578
\(115\) −4.39987 + 1.90819i −0.410290 + 0.177940i
\(116\) 3.07488 0.285495
\(117\) −1.92403 4.21304i −0.177877 0.389496i
\(118\) 14.1250 4.14748i 1.30031 0.381806i
\(119\) 10.1650 11.7310i 0.931825 1.07538i
\(120\) −0.841254 0.540641i −0.0767956 0.0493535i
\(121\) 5.85501 + 6.75704i 0.532274 + 0.614277i
\(122\) 1.20577 + 8.38634i 0.109166 + 0.759264i
\(123\) 2.92906 + 0.860051i 0.264105 + 0.0775482i
\(124\) −8.27071 + 5.31526i −0.742732 + 0.477325i
\(125\) −0.142315 + 0.989821i −0.0127290 + 0.0885323i
\(126\) 1.95003 4.26998i 0.173723 0.380400i
\(127\) −3.46102 + 7.57857i −0.307116 + 0.672490i −0.998762 0.0497469i \(-0.984159\pi\)
0.691646 + 0.722237i \(0.256886\pi\)
\(128\) −0.142315 + 0.989821i −0.0125790 + 0.0874887i
\(129\) −3.61113 + 2.32073i −0.317942 + 0.204329i
\(130\) 4.44398 + 1.30487i 0.389763 + 0.114445i
\(131\) 2.23897 + 15.5724i 0.195620 + 1.36056i 0.816811 + 0.576906i \(0.195740\pi\)
−0.621191 + 0.783659i \(0.713351\pi\)
\(132\) 0.939708 + 1.08448i 0.0817911 + 0.0943919i
\(133\) −16.6369 10.6919i −1.44260 0.927104i
\(134\) 7.78704 8.98673i 0.672698 0.776335i
\(135\) 0.959493 0.281733i 0.0825800 0.0242477i
\(136\) −1.37367 3.00791i −0.117791 0.257926i
\(137\) −4.08410 −0.348928 −0.174464 0.984664i \(-0.555819\pi\)
−0.174464 + 0.984664i \(0.555819\pi\)
\(138\) −4.75924 + 0.591308i −0.405133 + 0.0503355i
\(139\) −4.37740 −0.371286 −0.185643 0.982617i \(-0.559437\pi\)
−0.185643 + 0.982617i \(0.559437\pi\)
\(140\) 1.95003 + 4.26998i 0.164808 + 0.360879i
\(141\) 0.283153 0.0831412i 0.0238458 0.00700175i
\(142\) −7.83982 + 9.04763i −0.657903 + 0.759261i
\(143\) −5.59115 3.59321i −0.467555 0.300480i
\(144\) −0.654861 0.755750i −0.0545717 0.0629791i
\(145\) −0.437601 3.04358i −0.0363407 0.252755i
\(146\) 8.21183 + 2.41121i 0.679616 + 0.199553i
\(147\) −12.6486 + 8.12874i −1.04324 + 0.670447i
\(148\) 1.63081 11.3425i 0.134052 0.932352i
\(149\) −6.31785 + 13.8342i −0.517579 + 1.13334i 0.452769 + 0.891628i \(0.350436\pi\)
−0.970348 + 0.241712i \(0.922291\pi\)
\(150\) −0.415415 + 0.909632i −0.0339185 + 0.0742711i
\(151\) 1.54818 10.7678i 0.125989 0.876273i −0.824577 0.565750i \(-0.808587\pi\)
0.950566 0.310523i \(-0.100504\pi\)
\(152\) −3.54415 + 2.27769i −0.287468 + 0.184745i
\(153\) 3.17278 + 0.931613i 0.256504 + 0.0753165i
\(154\) −0.958637 6.66747i −0.0772492 0.537280i
\(155\) 6.43821 + 7.43009i 0.517129 + 0.596799i
\(156\) 3.89634 + 2.50403i 0.311957 + 0.200483i
\(157\) −10.2246 + 11.7998i −0.816011 + 0.941727i −0.999144 0.0413610i \(-0.986831\pi\)
0.183133 + 0.983088i \(0.441376\pi\)
\(158\) −13.1800 + 3.86999i −1.04854 + 0.307880i
\(159\) 5.58215 + 12.2232i 0.442693 + 0.969363i
\(160\) 1.00000 0.0790569
\(161\) 20.2949 + 9.74324i 1.59946 + 0.767875i
\(162\) 1.00000 0.0785674
\(163\) 4.17031 + 9.13171i 0.326644 + 0.715251i 0.999704 0.0243373i \(-0.00774756\pi\)
−0.673060 + 0.739588i \(0.735020\pi\)
\(164\) −2.92906 + 0.860051i −0.228721 + 0.0671587i
\(165\) 0.939708 1.08448i 0.0731562 0.0844267i
\(166\) 7.86619 + 5.05530i 0.610535 + 0.392367i
\(167\) −7.34209 8.47322i −0.568148 0.655678i 0.396866 0.917877i \(-0.370098\pi\)
−0.965014 + 0.262199i \(0.915552\pi\)
\(168\) 0.668052 + 4.64640i 0.0515413 + 0.358478i
\(169\) −8.10929 2.38110i −0.623791 0.183162i
\(170\) −2.78180 + 1.78775i −0.213354 + 0.137114i
\(171\) 0.599564 4.17006i 0.0458498 0.318892i
\(172\) 1.78319 3.90465i 0.135967 0.297726i
\(173\) 4.37809 9.58667i 0.332860 0.728861i −0.667009 0.745050i \(-0.732426\pi\)
0.999869 + 0.0161882i \(0.00515308\pi\)
\(174\) 0.437601 3.04358i 0.0331744 0.230733i
\(175\) 3.94900 2.53787i 0.298516 0.191845i
\(176\) −1.37685 0.404279i −0.103784 0.0304737i
\(177\) −2.09506 14.5715i −0.157475 1.09526i
\(178\) −3.64285 4.20407i −0.273043 0.315108i
\(179\) 11.5446 + 7.41928i 0.862886 + 0.554543i 0.895569 0.444923i \(-0.146769\pi\)
−0.0326832 + 0.999466i \(0.510405\pi\)
\(180\) −0.654861 + 0.755750i −0.0488104 + 0.0563302i
\(181\) −6.07936 + 1.78506i −0.451875 + 0.132683i −0.499748 0.866171i \(-0.666574\pi\)
0.0478725 + 0.998853i \(0.484756\pi\)
\(182\) −9.03176 19.7768i −0.669479 1.46595i
\(183\) 8.47258 0.626311
\(184\) 3.68404 3.07048i 0.271591 0.226359i
\(185\) −11.4592 −0.842496
\(186\) 4.08412 + 8.94297i 0.299462 + 0.655730i
\(187\) 4.55286 1.33684i 0.332938 0.0977595i
\(188\) −0.193254 + 0.223027i −0.0140945 + 0.0162659i
\(189\) −3.94900 2.53787i −0.287247 0.184603i
\(190\) 2.75889 + 3.18393i 0.200151 + 0.230986i
\(191\) −1.84961 12.8643i −0.133833 0.930830i −0.940493 0.339814i \(-0.889636\pi\)
0.806660 0.591016i \(-0.201273\pi\)
\(192\) 0.959493 + 0.281733i 0.0692454 + 0.0203323i
\(193\) −7.52332 + 4.83494i −0.541541 + 0.348027i −0.782641 0.622473i \(-0.786128\pi\)
0.241101 + 0.970500i \(0.422492\pi\)
\(194\) 1.46744 10.2063i 0.105356 0.732768i
\(195\) 1.92403 4.21304i 0.137783 0.301702i
\(196\) 6.24592 13.6767i 0.446137 0.976904i
\(197\) 1.51397 10.5299i 0.107866 0.750222i −0.862057 0.506811i \(-0.830824\pi\)
0.969923 0.243412i \(-0.0782665\pi\)
\(198\) 1.20718 0.775805i 0.0857903 0.0551341i
\(199\) −24.3900 7.16156i −1.72896 0.507670i −0.742248 0.670125i \(-0.766241\pi\)
−0.986716 + 0.162455i \(0.948059\pi\)
\(200\) −0.142315 0.989821i −0.0100632 0.0699909i
\(201\) −7.78704 8.98673i −0.549256 0.633875i
\(202\) −1.92412 1.23656i −0.135381 0.0870039i
\(203\) −9.45228 + 10.9085i −0.663420 + 0.765628i
\(204\) −3.17278 + 0.931613i −0.222139 + 0.0652260i
\(205\) 1.26815 + 2.77685i 0.0885712 + 0.193944i
\(206\) −0.108187 −0.00753774
\(207\) −0.0920206 + 4.79495i −0.00639587 + 0.333272i
\(208\) −4.63159 −0.321143
\(209\) −2.51137 5.49914i −0.173715 0.380383i
\(210\) 4.50404 1.32250i 0.310808 0.0912615i
\(211\) 2.56520 2.96040i 0.176596 0.203803i −0.660550 0.750782i \(-0.729677\pi\)
0.837146 + 0.546979i \(0.184222\pi\)
\(212\) −11.3044 7.26487i −0.776387 0.498954i
\(213\) 7.83982 + 9.04763i 0.537176 + 0.619934i
\(214\) 1.72893 + 12.0250i 0.118187 + 0.822009i
\(215\) −4.11868 1.20935i −0.280891 0.0824772i
\(216\) −0.841254 + 0.540641i −0.0572401 + 0.0367859i
\(217\) 6.56790 45.6807i 0.445858 3.10101i
\(218\) 0.350192 0.766814i 0.0237180 0.0519352i
\(219\) 3.55533 7.78509i 0.240247 0.526068i
\(220\) −0.204218 + 1.42037i −0.0137684 + 0.0957612i
\(221\) 12.8842 8.28014i 0.866682 0.556983i
\(222\) −10.9950 3.22843i −0.737937 0.216678i
\(223\) 2.27890 + 15.8501i 0.152606 + 1.06140i 0.911829 + 0.410569i \(0.134670\pi\)
−0.759223 + 0.650831i \(0.774421\pi\)
\(224\) −3.07404 3.54763i −0.205393 0.237036i
\(225\) 0.841254 + 0.540641i 0.0560836 + 0.0360427i
\(226\) 8.19344 9.45573i 0.545019 0.628986i
\(227\) 9.45746 2.77696i 0.627714 0.184313i 0.0476231 0.998865i \(-0.484835\pi\)
0.580090 + 0.814552i \(0.303017\pi\)
\(228\) 1.75012 + 3.83222i 0.115904 + 0.253795i
\(229\) 9.28423 0.613519 0.306760 0.951787i \(-0.400755\pi\)
0.306760 + 0.951787i \(0.400755\pi\)
\(230\) −3.56352 3.20957i −0.234972 0.211633i
\(231\) −6.73603 −0.443198
\(232\) 1.27735 + 2.79701i 0.0838621 + 0.183632i
\(233\) −22.5586 + 6.62380i −1.47786 + 0.433940i −0.918646 0.395082i \(-0.870716\pi\)
−0.559217 + 0.829021i \(0.688898\pi\)
\(234\) 3.03305 3.50032i 0.198277 0.228823i
\(235\) 0.248260 + 0.159547i 0.0161947 + 0.0104077i
\(236\) 9.64042 + 11.1256i 0.627538 + 0.724217i
\(237\) 1.95489 + 13.5966i 0.126984 + 0.883194i
\(238\) 14.8936 + 4.37317i 0.965411 + 0.283470i
\(239\) 2.07543 1.33380i 0.134248 0.0862762i −0.471793 0.881709i \(-0.656393\pi\)
0.606041 + 0.795433i \(0.292757\pi\)
\(240\) 0.142315 0.989821i 0.00918638 0.0638927i
\(241\) −2.77875 + 6.08462i −0.178995 + 0.391945i −0.977769 0.209687i \(-0.932755\pi\)
0.798773 + 0.601632i \(0.205483\pi\)
\(242\) −3.71416 + 8.13288i −0.238755 + 0.522802i
\(243\) 0.142315 0.989821i 0.00912950 0.0634971i
\(244\) −7.12759 + 4.58062i −0.456297 + 0.293244i
\(245\) −14.4263 4.23595i −0.921665 0.270625i
\(246\) 0.434447 + 3.02165i 0.0276994 + 0.192653i
\(247\) −12.7780 14.7466i −0.813047 0.938306i
\(248\) −8.27071 5.31526i −0.525191 0.337520i
\(249\) 6.12332 7.06668i 0.388049 0.447833i
\(250\) −0.959493 + 0.281733i −0.0606837 + 0.0178183i
\(251\) −4.02365 8.81056i −0.253970 0.556118i 0.739106 0.673589i \(-0.235248\pi\)
−0.993076 + 0.117472i \(0.962521\pi\)
\(252\) 4.69418 0.295706
\(253\) 3.60886 + 5.85974i 0.226887 + 0.368399i
\(254\) −8.33147 −0.522763
\(255\) 1.37367 + 3.00791i 0.0860223 + 0.188362i
\(256\) −0.959493 + 0.281733i −0.0599683 + 0.0176083i
\(257\) −0.979816 + 1.13077i −0.0611192 + 0.0705354i −0.785486 0.618880i \(-0.787587\pi\)
0.724367 + 0.689415i \(0.242132\pi\)
\(258\) −3.61113 2.32073i −0.224819 0.144482i
\(259\) 35.2260 + 40.6529i 2.18883 + 2.52605i
\(260\) 0.659144 + 4.58445i 0.0408784 + 0.284315i
\(261\) −2.95032 0.866293i −0.182620 0.0536222i
\(262\) −13.2350 + 8.50564i −0.817663 + 0.525480i
\(263\) −2.76936 + 19.2614i −0.170766 + 1.18771i 0.706504 + 0.707709i \(0.250271\pi\)
−0.877270 + 0.479997i \(0.840638\pi\)
\(264\) −0.596110 + 1.30530i −0.0366880 + 0.0803355i
\(265\) −5.58215 + 12.2232i −0.342909 + 0.750865i
\(266\) 2.81446 19.5750i 0.172566 1.20022i
\(267\) −4.67971 + 3.00747i −0.286394 + 0.184054i
\(268\) 11.4095 + 3.35012i 0.696944 + 0.204641i
\(269\) 4.63641 + 32.2469i 0.282687 + 1.96613i 0.256799 + 0.966465i \(0.417332\pi\)
0.0258878 + 0.999665i \(0.491759\pi\)
\(270\) 0.654861 + 0.755750i 0.0398536 + 0.0459935i
\(271\) 18.9683 + 12.1902i 1.15224 + 0.740501i 0.970084 0.242769i \(-0.0780556\pi\)
0.182157 + 0.983269i \(0.441692\pi\)
\(272\) 2.16545 2.49906i 0.131300 0.151528i
\(273\) −20.8609 + 6.12530i −1.26256 + 0.370720i
\(274\) −1.69659 3.71502i −0.102495 0.224433i
\(275\) 1.43497 0.0865322
\(276\) −2.51493 4.08352i −0.151381 0.245799i
\(277\) 12.6591 0.760612 0.380306 0.924861i \(-0.375819\pi\)
0.380306 + 0.924861i \(0.375819\pi\)
\(278\) −1.81844 3.98182i −0.109063 0.238814i
\(279\) 9.43317 2.76983i 0.564749 0.165825i
\(280\) −3.07404 + 3.54763i −0.183709 + 0.212011i
\(281\) 7.70029 + 4.94867i 0.459361 + 0.295213i 0.749781 0.661686i \(-0.230159\pi\)
−0.290420 + 0.956899i \(0.593795\pi\)
\(282\) 0.193254 + 0.223027i 0.0115081 + 0.0132811i
\(283\) 0.403864 + 2.80894i 0.0240072 + 0.166974i 0.998298 0.0583208i \(-0.0185746\pi\)
−0.974291 + 0.225295i \(0.927666\pi\)
\(284\) −11.4868 3.37283i −0.681616 0.200141i
\(285\) 3.54415 2.27769i 0.209937 0.134918i
\(286\) 0.945855 6.57856i 0.0559296 0.388999i
\(287\) 5.95291 13.0351i 0.351389 0.769435i
\(288\) 0.415415 0.909632i 0.0244786 0.0536006i
\(289\) 0.863216 6.00380i 0.0507774 0.353165i
\(290\) 2.58675 1.66240i 0.151899 0.0976197i
\(291\) −9.89356 2.90501i −0.579971 0.170295i
\(292\) 1.21800 + 8.47140i 0.0712782 + 0.495751i
\(293\) −7.91301 9.13210i −0.462283 0.533503i 0.475966 0.879464i \(-0.342098\pi\)
−0.938249 + 0.345961i \(0.887553\pi\)
\(294\) −12.6486 8.12874i −0.737679 0.474078i
\(295\) 9.64042 11.1256i 0.561287 0.647760i
\(296\) 10.9950 3.22843i 0.639072 0.187648i
\(297\) −0.596110 1.30530i −0.0345898 0.0757411i
\(298\) −15.2085 −0.881007
\(299\) 16.5048 + 14.8654i 0.954495 + 0.859689i
\(300\) −1.00000 −0.0577350
\(301\) 8.37063 + 18.3291i 0.482475 + 1.05647i
\(302\) 10.4379 3.06484i 0.600633 0.176362i
\(303\) −1.49780 + 1.72856i −0.0860465 + 0.0993030i
\(304\) −3.54415 2.27769i −0.203271 0.130634i
\(305\) 5.54836 + 6.40315i 0.317698 + 0.366643i
\(306\) 0.470597 + 3.27307i 0.0269022 + 0.187109i
\(307\) 6.16998 + 1.81167i 0.352140 + 0.103398i 0.453018 0.891501i \(-0.350347\pi\)
−0.100879 + 0.994899i \(0.532165\pi\)
\(308\) 5.66671 3.64177i 0.322891 0.207509i
\(309\) −0.0153966 + 0.107086i −0.000875882 + 0.00609189i
\(310\) −4.08412 + 8.94297i −0.231962 + 0.507926i
\(311\) 2.22162 4.86466i 0.125976 0.275850i −0.836126 0.548537i \(-0.815185\pi\)
0.962103 + 0.272687i \(0.0879124\pi\)
\(312\) −0.659144 + 4.58445i −0.0373167 + 0.259543i
\(313\) 19.8143 12.7339i 1.11997 0.719763i 0.156529 0.987673i \(-0.449970\pi\)
0.963444 + 0.267911i \(0.0863332\pi\)
\(314\) −14.9809 4.39880i −0.845423 0.248239i
\(315\) −0.668052 4.64640i −0.0376405 0.261795i
\(316\) −8.99543 10.3813i −0.506033 0.583993i
\(317\) −9.76031 6.27257i −0.548194 0.352303i 0.237042 0.971499i \(-0.423822\pi\)
−0.785236 + 0.619197i \(0.787458\pi\)
\(318\) −8.79971 + 10.1554i −0.493463 + 0.569487i
\(319\) −4.23363 + 1.24311i −0.237038 + 0.0696007i
\(320\) 0.415415 + 0.909632i 0.0232224 + 0.0508500i
\(321\) 12.1486 0.678069
\(322\) −0.431961 + 22.5084i −0.0240723 + 1.25434i
\(323\) 13.9310 0.775144
\(324\) 0.415415 + 0.909632i 0.0230786 + 0.0505351i
\(325\) 4.44398 1.30487i 0.246508 0.0723812i
\(326\) −6.57409 + 7.58690i −0.364105 + 0.420200i
\(327\) −0.709171 0.455757i −0.0392173 0.0252034i
\(328\) −1.99911 2.30709i −0.110382 0.127388i
\(329\) −0.197147 1.37119i −0.0108690 0.0755959i
\(330\) 1.37685 + 0.404279i 0.0757929 + 0.0222548i
\(331\) 16.6020 10.6695i 0.912529 0.586447i 0.00204816 0.999998i \(-0.499348\pi\)
0.910481 + 0.413551i \(0.135712\pi\)
\(332\) −1.33072 + 9.25539i −0.0730329 + 0.507955i
\(333\) −4.76032 + 10.4236i −0.260864 + 0.571212i
\(334\) 4.65750 10.1985i 0.254847 0.558037i
\(335\) 1.69229 11.7701i 0.0924595 0.643070i
\(336\) −3.94900 + 2.53787i −0.215436 + 0.138452i
\(337\) −4.79352 1.40750i −0.261120 0.0766717i 0.148552 0.988905i \(-0.452539\pi\)
−0.409672 + 0.912233i \(0.634357\pi\)
\(338\) −1.20279 8.36561i −0.0654233 0.455029i
\(339\) −8.19344 9.45573i −0.445006 0.513565i
\(340\) −2.78180 1.78775i −0.150864 0.0969545i
\(341\) 9.23866 10.6620i 0.500301 0.577379i
\(342\) 4.04228 1.18692i 0.218582 0.0641814i
\(343\) 15.6693 + 34.3109i 0.846060 + 1.85261i
\(344\) 4.29256 0.231439
\(345\) −3.68404 + 3.07048i −0.198342 + 0.165309i
\(346\) 10.5391 0.566584
\(347\) 7.10506 + 15.5579i 0.381419 + 0.835192i 0.998821 + 0.0485439i \(0.0154581\pi\)
−0.617402 + 0.786648i \(0.711815\pi\)
\(348\) 2.95032 0.866293i 0.158154 0.0464382i
\(349\) 6.22054 7.17889i 0.332978 0.384277i −0.564428 0.825482i \(-0.690903\pi\)
0.897406 + 0.441205i \(0.145449\pi\)
\(350\) 3.94900 + 2.53787i 0.211083 + 0.135655i
\(351\) −3.03305 3.50032i −0.161892 0.186833i
\(352\) −0.204218 1.42037i −0.0108849 0.0757059i
\(353\) −4.17976 1.22729i −0.222466 0.0653220i 0.168600 0.985685i \(-0.446075\pi\)
−0.391066 + 0.920363i \(0.627894\pi\)
\(354\) 12.3844 7.95895i 0.658222 0.423013i
\(355\) −1.70376 + 11.8499i −0.0904260 + 0.628926i
\(356\) 2.31086 5.06008i 0.122475 0.268184i
\(357\) 6.44824 14.1197i 0.341277 0.747292i
\(358\) −1.95300 + 13.5834i −0.103219 + 0.717907i
\(359\) −11.3677 + 7.30559i −0.599965 + 0.385574i −0.805082 0.593163i \(-0.797879\pi\)
0.205117 + 0.978737i \(0.434243\pi\)
\(360\) −0.959493 0.281733i −0.0505697 0.0148486i
\(361\) 0.178058 + 1.23842i 0.00937148 + 0.0651800i
\(362\) −4.14921 4.78844i −0.218078 0.251675i
\(363\) 7.52152 + 4.83379i 0.394778 + 0.253708i
\(364\) 14.2377 16.4312i 0.746257 0.861227i
\(365\) 8.21183 2.41121i 0.429827 0.126209i
\(366\) 3.51964 + 7.70693i 0.183974 + 0.402848i
\(367\) 21.8299 1.13951 0.569755 0.821814i \(-0.307038\pi\)
0.569755 + 0.821814i \(0.307038\pi\)
\(368\) 4.32341 + 2.07560i 0.225373 + 0.108198i
\(369\) 3.05272 0.158918
\(370\) −4.76032 10.4236i −0.247477 0.541899i
\(371\) 60.5231 17.7712i 3.14220 0.922634i
\(372\) −6.43821 + 7.43009i −0.333805 + 0.385232i
\(373\) 4.98037 + 3.20069i 0.257874 + 0.165725i 0.663190 0.748451i \(-0.269202\pi\)
−0.405316 + 0.914177i \(0.632839\pi\)
\(374\) 3.10736 + 3.58608i 0.160678 + 0.185432i
\(375\) 0.142315 + 0.989821i 0.00734911 + 0.0511142i
\(376\) −0.283153 0.0831412i −0.0146025 0.00428768i
\(377\) −11.9808 + 7.69957i −0.617041 + 0.396548i
\(378\) 0.668052 4.64640i 0.0343609 0.238985i
\(379\) 5.57525 12.2081i 0.286381 0.627087i −0.710695 0.703500i \(-0.751619\pi\)
0.997076 + 0.0764129i \(0.0243467\pi\)
\(380\) −1.75012 + 3.83222i −0.0897791 + 0.196589i
\(381\) −1.18569 + 8.24667i −0.0607448 + 0.422490i
\(382\) 10.9334 7.02650i 0.559404 0.359507i
\(383\) 19.6524 + 5.77045i 1.00419 + 0.294856i 0.742174 0.670207i \(-0.233795\pi\)
0.262015 + 0.965064i \(0.415613\pi\)
\(384\) 0.142315 + 0.989821i 0.00726247 + 0.0505116i
\(385\) −4.41116 5.09075i −0.224814 0.259449i
\(386\) −7.52332 4.83494i −0.382927 0.246092i
\(387\) −2.81103 + 3.24410i −0.142892 + 0.164907i
\(388\) 9.89356 2.90501i 0.502269 0.147480i
\(389\) 5.13476 + 11.2435i 0.260343 + 0.570071i 0.993991 0.109458i \(-0.0349116\pi\)
−0.733649 + 0.679529i \(0.762184\pi\)
\(390\) 4.63159 0.234530
\(391\) −15.7375 + 1.95530i −0.795880 + 0.0988836i
\(392\) 15.0354 0.759401
\(393\) 6.53552 + 14.3108i 0.329673 + 0.721884i
\(394\) 10.2072 2.99711i 0.514233 0.150992i
\(395\) −8.99543 + 10.3813i −0.452609 + 0.522339i
\(396\) 1.20718 + 0.775805i 0.0606629 + 0.0389857i
\(397\) −2.77121 3.19814i −0.139083 0.160510i 0.681935 0.731413i \(-0.261139\pi\)
−0.821018 + 0.570903i \(0.806593\pi\)
\(398\) −3.61760 25.1610i −0.181334 1.26121i
\(399\) −18.9752 5.57163i −0.949950 0.278930i
\(400\) 0.841254 0.540641i 0.0420627 0.0270320i
\(401\) −4.12020 + 28.6566i −0.205753 + 1.43104i 0.581064 + 0.813858i \(0.302636\pi\)
−0.786817 + 0.617186i \(0.788273\pi\)
\(402\) 4.93976 10.8166i 0.246373 0.539481i
\(403\) 18.9160 41.4202i 0.942271 2.06329i
\(404\) 0.325504 2.26393i 0.0161944 0.112635i
\(405\) 0.841254 0.540641i 0.0418022 0.0268647i
\(406\) −13.8494 4.06654i −0.687332 0.201819i
\(407\) 2.34017 + 16.2763i 0.115998 + 0.806784i
\(408\) −2.16545 2.49906i −0.107206 0.123722i
\(409\) 10.7850 + 6.93110i 0.533284 + 0.342721i 0.779407 0.626518i \(-0.215520\pi\)
−0.246123 + 0.969239i \(0.579157\pi\)
\(410\) −1.99911 + 2.30709i −0.0987289 + 0.113939i
\(411\) −3.91866 + 1.15062i −0.193293 + 0.0567560i
\(412\) −0.0449425 0.0984103i −0.00221416 0.00484833i
\(413\) −69.1046 −3.40042
\(414\) −4.39987 + 1.90819i −0.216242 + 0.0937824i
\(415\) 9.35056 0.459001
\(416\) −1.92403 4.21304i −0.0943335 0.206561i
\(417\) −4.20008 + 1.23326i −0.205679 + 0.0603928i
\(418\) 3.95893 4.56885i 0.193638 0.223470i
\(419\) −1.99134 1.27976i −0.0972835 0.0625203i 0.491095 0.871106i \(-0.336597\pi\)
−0.588378 + 0.808586i \(0.700233\pi\)
\(420\) 3.07404 + 3.54763i 0.149998 + 0.173107i
\(421\) −3.47036 24.1369i −0.169135 1.17636i −0.880677 0.473717i \(-0.842912\pi\)
0.711542 0.702644i \(-0.247997\pi\)
\(422\) 3.75850 + 1.10360i 0.182961 + 0.0537222i
\(423\) 0.248260 0.159547i 0.0120708 0.00775743i
\(424\) 1.91236 13.3007i 0.0928724 0.645941i
\(425\) −1.37367 + 3.00791i −0.0666325 + 0.145905i
\(426\) −4.97324 + 10.8899i −0.240954 + 0.527616i
\(427\) 5.66013 39.3670i 0.273913 1.90510i
\(428\) −10.2201 + 6.56803i −0.494005 + 0.317478i
\(429\) −6.37699 1.87245i −0.307884 0.0904029i
\(430\) −0.610894 4.24886i −0.0294599 0.204898i
\(431\) −6.14310 7.08952i −0.295903 0.341490i 0.588258 0.808674i \(-0.299814\pi\)
−0.884160 + 0.467184i \(0.845269\pi\)
\(432\) −0.841254 0.540641i −0.0404748 0.0260116i
\(433\) 8.42055 9.71783i 0.404666 0.467009i −0.516439 0.856324i \(-0.672743\pi\)
0.921105 + 0.389315i \(0.127288\pi\)
\(434\) 44.2811 13.0021i 2.12556 0.624120i
\(435\) −1.27735 2.79701i −0.0612442 0.134106i
\(436\) 0.842993 0.0403721
\(437\) 5.31926 + 19.4918i 0.254454 + 0.932418i
\(438\) 8.55851 0.408941
\(439\) −3.53332 7.73689i −0.168636 0.369261i 0.806379 0.591399i \(-0.201424\pi\)
−0.975015 + 0.222137i \(0.928697\pi\)
\(440\) −1.37685 + 0.404279i −0.0656386 + 0.0192732i
\(441\) −9.84608 + 11.3630i −0.468861 + 0.541094i
\(442\) 12.8842 + 8.28014i 0.612837 + 0.393846i
\(443\) −5.05439 5.83307i −0.240141 0.277138i 0.622867 0.782328i \(-0.285968\pi\)
−0.863008 + 0.505190i \(0.831422\pi\)
\(444\) −1.63081 11.3425i −0.0773949 0.538293i
\(445\) −5.33745 1.56722i −0.253019 0.0742932i
\(446\) −13.4711 + 8.65732i −0.637873 + 0.409936i
\(447\) −2.16440 + 15.0537i −0.102373 + 0.712017i
\(448\) 1.95003 4.26998i 0.0921305 0.201738i
\(449\) −11.6378 + 25.4832i −0.549221 + 1.20263i 0.407924 + 0.913016i \(0.366253\pi\)
−0.957145 + 0.289610i \(0.906474\pi\)
\(450\) −0.142315 + 0.989821i −0.00670879 + 0.0466606i
\(451\) 3.68517 2.36832i 0.173528 0.111520i
\(452\) 12.0049 + 3.52496i 0.564664 + 0.165800i
\(453\) −1.54818 10.7678i −0.0727398 0.505917i
\(454\) 6.45478 + 7.44922i 0.302938 + 0.349609i
\(455\) −18.2902 11.7544i −0.857456 0.551053i
\(456\) −2.75889 + 3.18393i −0.129197 + 0.149101i
\(457\) −12.3929 + 3.63887i −0.579714 + 0.170219i −0.558426 0.829554i \(-0.688595\pi\)
−0.0212874 + 0.999773i \(0.506777\pi\)
\(458\) 3.85681 + 8.44523i 0.180217 + 0.394620i
\(459\) 3.30673 0.154345
\(460\) 1.43919 4.57479i 0.0671024 0.213301i
\(461\) −12.0148 −0.559585 −0.279792 0.960060i \(-0.590266\pi\)
−0.279792 + 0.960060i \(0.590266\pi\)
\(462\) −2.79825 6.12731i −0.130186 0.285068i
\(463\) −0.686756 + 0.201650i −0.0319162 + 0.00937145i −0.297652 0.954675i \(-0.596203\pi\)
0.265735 + 0.964046i \(0.414385\pi\)
\(464\) −2.01362 + 2.32384i −0.0934798 + 0.107881i
\(465\) 8.27071 + 5.31526i 0.383545 + 0.246489i
\(466\) −15.3964 17.7684i −0.713225 0.823105i
\(467\) 0.466386 + 3.24379i 0.0215818 + 0.150104i 0.997763 0.0668529i \(-0.0212958\pi\)
−0.976181 + 0.216957i \(0.930387\pi\)
\(468\) 4.44398 + 1.30487i 0.205423 + 0.0603176i
\(469\) −46.9581 + 30.1781i −2.16832 + 1.39350i
\(470\) −0.0419981 + 0.292103i −0.00193723 + 0.0134737i
\(471\) −6.48603 + 14.2024i −0.298861 + 0.654413i
\(472\) −6.11546 + 13.3910i −0.281487 + 0.616370i
\(473\) −0.876617 + 6.09701i −0.0403069 + 0.280341i
\(474\) −11.5558 + 7.42646i −0.530776 + 0.341109i
\(475\) 4.04228 + 1.18692i 0.185473 + 0.0544597i
\(476\) 2.20907 + 15.3644i 0.101252 + 0.704226i
\(477\) 8.79971 + 10.1554i 0.402911 + 0.464984i
\(478\) 2.07543 + 1.33380i 0.0949279 + 0.0610065i
\(479\) 8.22471 9.49182i 0.375796 0.433692i −0.536074 0.844171i \(-0.680093\pi\)
0.911870 + 0.410479i \(0.134638\pi\)
\(480\) 0.959493 0.281733i 0.0437947 0.0128593i
\(481\) 22.0478 + 48.2780i 1.00530 + 2.20129i
\(482\) −6.68910 −0.304680
\(483\) 22.2178 + 3.63084i 1.01094 + 0.165209i
\(484\) −8.94085 −0.406402
\(485\) −4.28344 9.37943i −0.194501 0.425898i
\(486\) 0.959493 0.281733i 0.0435235 0.0127796i
\(487\) −0.713730 + 0.823688i −0.0323422 + 0.0373249i −0.771690 0.635999i \(-0.780588\pi\)
0.739348 + 0.673323i \(0.235134\pi\)
\(488\) −7.12759 4.58062i −0.322651 0.207355i
\(489\) 6.57409 + 7.58690i 0.297290 + 0.343092i
\(490\) −2.13976 14.8823i −0.0966644 0.672315i
\(491\) 16.1781 + 4.75032i 0.730107 + 0.214379i 0.625599 0.780145i \(-0.284855\pi\)
0.104509 + 0.994524i \(0.466673\pi\)
\(492\) −2.56811 + 1.65043i −0.115779 + 0.0744069i
\(493\) 1.44703 10.0643i 0.0651708 0.453273i
\(494\) 8.10583 17.7493i 0.364699 0.798578i
\(495\) 0.596110 1.30530i 0.0267931 0.0586688i
\(496\) 1.39916 9.73134i 0.0628240 0.436950i
\(497\) 47.2764 30.3827i 2.12064 1.36285i
\(498\) 8.97180 + 2.63436i 0.402036 + 0.118048i
\(499\) −5.69078 39.5803i −0.254754 1.77186i −0.568828 0.822457i \(-0.692603\pi\)
0.314073 0.949399i \(-0.398306\pi\)
\(500\) −0.654861 0.755750i −0.0292863 0.0337981i
\(501\) −9.43186 6.06149i −0.421385 0.270807i
\(502\) 6.34289 7.32008i 0.283097 0.326711i
\(503\) −6.23722 + 1.83141i −0.278104 + 0.0816587i −0.417810 0.908534i \(-0.637202\pi\)
0.139706 + 0.990193i \(0.455384\pi\)
\(504\) 1.95003 + 4.26998i 0.0868615 + 0.190200i
\(505\) −2.28721 −0.101779
\(506\) −3.83103 + 5.71696i −0.170310 + 0.254150i
\(507\) −8.45164 −0.375350
\(508\) −3.46102 7.57857i −0.153558 0.336245i
\(509\) 10.4018 3.05425i 0.461053 0.135377i −0.0429538 0.999077i \(-0.513677\pi\)
0.504007 + 0.863700i \(0.331859\pi\)
\(510\) −2.16545 + 2.49906i −0.0958876 + 0.110660i
\(511\) −33.7975 21.7204i −1.49512 0.960852i
\(512\) −0.654861 0.755750i −0.0289410 0.0333997i
\(513\) −0.599564 4.17006i −0.0264714 0.184112i
\(514\) −1.43561 0.421534i −0.0633222 0.0185931i
\(515\) −0.0910126 + 0.0584902i −0.00401049 + 0.00257739i
\(516\) 0.610894 4.24886i 0.0268931 0.187046i
\(517\) 0.175916 0.385202i 0.00773678 0.0169412i
\(518\) −22.3458 + 48.9305i −0.981818 + 2.14988i
\(519\) 1.49987 10.4318i 0.0658368 0.457905i
\(520\) −3.89634 + 2.50403i −0.170866 + 0.109809i
\(521\) −1.79668 0.527553i −0.0787139 0.0231125i 0.242138 0.970242i \(-0.422151\pi\)
−0.320852 + 0.947129i \(0.603969\pi\)
\(522\) −0.437601 3.04358i −0.0191533 0.133214i
\(523\) −15.4425 17.8216i −0.675255 0.779286i 0.309934 0.950758i \(-0.399693\pi\)
−0.985189 + 0.171472i \(0.945148\pi\)
\(524\) −13.2350 8.50564i −0.578175 0.371571i
\(525\) 3.07404 3.54763i 0.134162 0.154831i
\(526\) −18.6712 + 5.48235i −0.814102 + 0.239042i
\(527\) 13.5051 + 29.5720i 0.588290 + 1.28818i
\(528\) −1.43497 −0.0624492
\(529\) −8.74479 21.2727i −0.380208 0.924901i
\(530\) −13.4375 −0.583689
\(531\) −6.11546 13.3910i −0.265388 0.581120i
\(532\) 18.9752 5.57163i 0.822681 0.241561i
\(533\) 9.25905 10.6855i 0.401054 0.462841i
\(534\) −4.67971 3.00747i −0.202511 0.130146i
\(535\) 7.95565 + 9.18131i 0.343953 + 0.396943i
\(536\) 1.69229 + 11.7701i 0.0730956 + 0.508391i
\(537\) 13.1672 + 3.86625i 0.568208 + 0.166841i
\(538\) −27.4068 + 17.6133i −1.18159 + 0.759362i
\(539\) −3.07049 + 21.3558i −0.132256 + 0.919858i
\(540\) −0.415415 + 0.909632i −0.0178766 + 0.0391443i
\(541\) −2.89286 + 6.33447i −0.124374 + 0.272340i −0.961569 0.274564i \(-0.911466\pi\)
0.837195 + 0.546904i \(0.184194\pi\)
\(542\) −3.20886 + 22.3181i −0.137833 + 0.958646i
\(543\) −5.33020 + 3.42551i −0.228741 + 0.147003i
\(544\) 3.17278 + 0.931613i 0.136032 + 0.0399426i
\(545\) −0.119970 0.834413i −0.00513897 0.0357423i
\(546\) −14.2377 16.4312i −0.609317 0.703189i
\(547\) −16.9113 10.8682i −0.723075 0.464692i 0.126630 0.991950i \(-0.459584\pi\)
−0.849705 + 0.527258i \(0.823220\pi\)
\(548\) 2.67451 3.08655i 0.114250 0.131851i
\(549\) 8.12938 2.38700i 0.346954 0.101875i
\(550\) 0.596110 + 1.30530i 0.0254182 + 0.0556581i
\(551\) −12.9543 −0.551870
\(552\) 2.66976 3.98402i 0.113632 0.169571i
\(553\) 64.4812 2.74202
\(554\) 5.25878 + 11.5151i 0.223424 + 0.489231i
\(555\) −10.9950 + 3.22843i −0.466712 + 0.137039i
\(556\) 2.86659 3.30822i 0.121570 0.140300i
\(557\) −25.4637 16.3645i −1.07893 0.693386i −0.124620 0.992205i \(-0.539771\pi\)
−0.954310 + 0.298818i \(0.903408\pi\)
\(558\) 6.43821 + 7.43009i 0.272551 + 0.314541i
\(559\) 2.82941 + 19.6790i 0.119671 + 0.832333i
\(560\) −4.50404 1.32250i −0.190330 0.0558860i
\(561\) 3.99181 2.56538i 0.168534 0.108310i
\(562\) −1.30266 + 9.06018i −0.0549493 + 0.382181i
\(563\) 1.48002 3.24078i 0.0623752 0.136583i −0.875877 0.482534i \(-0.839716\pi\)
0.938252 + 0.345951i \(0.112444\pi\)
\(564\) −0.122592 + 0.268439i −0.00516204 + 0.0113033i
\(565\) 1.78060 12.3844i 0.0749106 0.521014i
\(566\) −2.38733 + 1.53424i −0.100347 + 0.0644890i
\(567\) −4.50404 1.32250i −0.189152 0.0555400i
\(568\) −1.70376 11.8499i −0.0714880 0.497210i
\(569\) −21.4803 24.7895i −0.900499 1.03923i −0.999027 0.0440971i \(-0.985959\pi\)
0.0985282 0.995134i \(-0.468587\pi\)
\(570\) 3.54415 + 2.27769i 0.148448 + 0.0954018i
\(571\) −22.2792 + 25.7115i −0.932354 + 1.07599i 0.0645926 + 0.997912i \(0.479425\pi\)
−0.996947 + 0.0780825i \(0.975120\pi\)
\(572\) 6.37699 1.87245i 0.266636 0.0782912i
\(573\) −5.39899 11.8221i −0.225546 0.493877i
\(574\) 14.3300 0.598124
\(575\) −4.73305 0.773476i −0.197382 0.0322562i
\(576\) 1.00000 0.0416667
\(577\) −8.41135 18.4183i −0.350169 0.766764i −0.999978 0.00666577i \(-0.997878\pi\)
0.649809 0.760098i \(-0.274849\pi\)
\(578\) 5.81984 1.70886i 0.242073 0.0710792i
\(579\) −5.85641 + 6.75866i −0.243384 + 0.280880i
\(580\) 2.58675 + 1.66240i 0.107409 + 0.0690276i
\(581\) −28.7440 33.1723i −1.19250 1.37622i
\(582\) −1.46744 10.2063i −0.0608274 0.423064i
\(583\) 18.5014 + 5.43251i 0.766250 + 0.224991i
\(584\) −7.19988 + 4.62708i −0.297933 + 0.191470i
\(585\) 0.659144 4.58445i 0.0272523 0.189544i
\(586\) 5.01967 10.9915i 0.207361 0.454056i
\(587\) 3.46741 7.59257i 0.143115 0.313379i −0.824477 0.565895i \(-0.808531\pi\)
0.967593 + 0.252516i \(0.0812581\pi\)
\(588\) 2.13976 14.8823i 0.0882421 0.613737i
\(589\) 34.8440 22.3929i 1.43572 0.922682i
\(590\) 14.1250 + 4.14748i 0.581518 + 0.170749i
\(591\) −1.51397 10.5299i −0.0622763 0.433141i
\(592\) 7.50417 + 8.66027i 0.308419 + 0.355935i
\(593\) −21.4703 13.7981i −0.881680 0.566621i 0.0196247 0.999807i \(-0.493753\pi\)
−0.901304 + 0.433186i \(0.857389\pi\)
\(594\) 0.939708 1.08448i 0.0385567 0.0444968i
\(595\) 14.8936 4.37317i 0.610580 0.179282i
\(596\) −6.31785 13.8342i −0.258789 0.566670i
\(597\) −25.4197 −1.04036
\(598\) −6.66572 + 21.1886i −0.272582 + 0.866465i
\(599\) −29.5317 −1.20663 −0.603317 0.797501i \(-0.706155\pi\)
−0.603317 + 0.797501i \(0.706155\pi\)
\(600\) −0.415415 0.909632i −0.0169592 0.0371356i
\(601\) −8.13090 + 2.38745i −0.331666 + 0.0973860i −0.443326 0.896360i \(-0.646202\pi\)
0.111660 + 0.993747i \(0.464383\pi\)
\(602\) −13.1955 + 15.2284i −0.537808 + 0.620663i
\(603\) −10.0035 6.42884i −0.407373 0.261802i
\(604\) 7.12394 + 8.22146i 0.289869 + 0.334527i
\(605\) 1.27242 + 8.84985i 0.0517311 + 0.359797i
\(606\) −2.19456 0.644381i −0.0891479 0.0261762i
\(607\) 28.5036 18.3182i 1.15693 0.743511i 0.185920 0.982565i \(-0.440473\pi\)
0.971006 + 0.239053i \(0.0768371\pi\)
\(608\) 0.599564 4.17006i 0.0243155 0.169118i
\(609\) −5.99612 + 13.1297i −0.242975 + 0.532041i
\(610\) −3.51964 + 7.70693i −0.142506 + 0.312044i
\(611\) 0.194518 1.35290i 0.00786935 0.0547325i
\(612\) −2.78180 + 1.78775i −0.112448 + 0.0722656i
\(613\) −23.5402 6.91203i −0.950781 0.279174i −0.230669 0.973032i \(-0.574091\pi\)
−0.720112 + 0.693858i \(0.755910\pi\)
\(614\) 0.915150 + 6.36501i 0.0369325 + 0.256871i
\(615\) 1.99911 + 2.30709i 0.0806118 + 0.0930309i
\(616\) 5.66671 + 3.64177i 0.228318 + 0.146731i
\(617\) 4.00623 4.62344i 0.161285 0.186133i −0.669355 0.742943i \(-0.733429\pi\)
0.830640 + 0.556810i \(0.187975\pi\)
\(618\) −0.103805 + 0.0304798i −0.00417563 + 0.00122608i
\(619\) 15.2937 + 33.4886i 0.614707 + 1.34602i 0.919308 + 0.393540i \(0.128750\pi\)
−0.304601 + 0.952480i \(0.598523\pi\)
\(620\) −9.83141 −0.394839
\(621\) 1.26260 + 4.62664i 0.0506664 + 0.185661i
\(622\) 5.34794 0.214433
\(623\) 10.8476 + 23.7530i 0.434601 + 0.951643i
\(624\) −4.44398 + 1.30487i −0.177902 + 0.0522366i
\(625\) −0.654861 + 0.755750i −0.0261944 + 0.0302300i
\(626\) 19.8143 + 12.7339i 0.791940 + 0.508949i
\(627\) −3.95893 4.56885i −0.158104 0.182462i
\(628\) −2.22202 15.4545i −0.0886681 0.616700i
\(629\) −36.3575 10.6755i −1.44967 0.425661i
\(630\) 3.94900 2.53787i 0.157332 0.101111i
\(631\) 4.81059 33.4584i 0.191507 1.33196i −0.636516 0.771264i \(-0.719625\pi\)
0.828022 0.560695i \(-0.189466\pi\)
\(632\) 5.70631 12.4951i 0.226985 0.497027i
\(633\) 1.62725 3.56319i 0.0646775 0.141624i
\(634\) 1.65115 11.4840i 0.0655756 0.456088i
\(635\) −7.00888 + 4.50433i −0.278139 + 0.178749i
\(636\) −12.8932 3.78579i −0.511249 0.150116i
\(637\) 9.91048 + 68.9289i 0.392667 + 2.73106i
\(638\) −2.88949 3.33464i −0.114396 0.132020i
\(639\) 10.0713 + 6.47241i 0.398413 + 0.256045i
\(640\) −0.654861 + 0.755750i −0.0258856 + 0.0298736i
\(641\) −20.9910 + 6.16352i −0.829095 + 0.243444i −0.668628 0.743597i \(-0.733118\pi\)
−0.160467 + 0.987041i \(0.551300\pi\)
\(642\) 5.04672 + 11.0508i 0.199178 + 0.436139i
\(643\) −40.5773 −1.60021 −0.800106 0.599859i \(-0.795223\pi\)
−0.800106 + 0.599859i \(0.795223\pi\)
\(644\) −20.6538 + 8.95739i −0.813873 + 0.352971i
\(645\) −4.29256 −0.169019
\(646\) 5.78717 + 12.6721i 0.227693 + 0.498578i
\(647\) 21.8834 6.42556i 0.860327 0.252615i 0.178331 0.983971i \(-0.442930\pi\)
0.681996 + 0.731356i \(0.261112\pi\)
\(648\) −0.654861 + 0.755750i −0.0257254 + 0.0296886i
\(649\) −17.7712 11.4209i −0.697582 0.448309i
\(650\) 3.03305 + 3.50032i 0.118966 + 0.137294i
\(651\) −6.56790 45.6807i −0.257416 1.79037i
\(652\) −9.63226 2.82829i −0.377229 0.110764i
\(653\) −12.0225 + 7.72640i −0.470478 + 0.302358i −0.754312 0.656516i \(-0.772030\pi\)
0.283835 + 0.958873i \(0.408393\pi\)
\(654\) 0.119970 0.834413i 0.00469122 0.0326281i
\(655\) −6.53552 + 14.3108i −0.255364 + 0.559169i
\(656\) 1.26815 2.77685i 0.0495128 0.108418i
\(657\) 1.21800 8.47140i 0.0475188 0.330501i
\(658\) 1.16538 0.748942i 0.0454311 0.0291968i
\(659\) 18.7366 + 5.50155i 0.729873 + 0.214310i 0.625496 0.780228i \(-0.284897\pi\)
0.104378 + 0.994538i \(0.466715\pi\)
\(660\) 0.204218 + 1.42037i 0.00794918 + 0.0552877i
\(661\) −3.62174 4.17971i −0.140869 0.162572i 0.680931 0.732348i \(-0.261575\pi\)
−0.821800 + 0.569776i \(0.807030\pi\)
\(662\) 16.6020 + 10.6695i 0.645256 + 0.414681i
\(663\) 10.0295 11.5746i 0.389512 0.449521i
\(664\) −8.97180 + 2.63436i −0.348173 + 0.102233i
\(665\) −8.21538 17.9892i −0.318579 0.697590i
\(666\) −11.4592 −0.444034
\(667\) 14.6341 1.81820i 0.566633 0.0704010i
\(668\) 11.2117 0.433793
\(669\) 6.65207 + 14.5660i 0.257184 + 0.563154i
\(670\) 11.4095 3.35012i 0.440786 0.129426i
\(671\) 7.96175 9.18835i 0.307360 0.354712i
\(672\) −3.94900 2.53787i −0.152336 0.0979004i
\(673\) 0.160246 + 0.184934i 0.00617705 + 0.00712869i 0.758830 0.651289i \(-0.225771\pi\)
−0.752653 + 0.658418i \(0.771226\pi\)
\(674\) −0.710989 4.94504i −0.0273863 0.190476i
\(675\) 0.959493 + 0.281733i 0.0369309 + 0.0108439i
\(676\) 7.10997 4.56930i 0.273460 0.175742i
\(677\) 2.58348 17.9685i 0.0992914 0.690587i −0.877996 0.478668i \(-0.841120\pi\)
0.977287 0.211919i \(-0.0679712\pi\)
\(678\) 5.19756 11.3811i 0.199611 0.437087i
\(679\) −20.1073 + 44.0288i −0.771646 + 1.68967i
\(680\) 0.470597 3.27307i 0.0180466 0.125517i
\(681\) 8.29201 5.32895i 0.317750 0.204206i
\(682\) 13.5364 + 3.97463i 0.518334 + 0.152197i
\(683\) 3.70090 + 25.7403i 0.141611 + 0.984925i 0.929425 + 0.369012i \(0.120304\pi\)
−0.787814 + 0.615913i \(0.788787\pi\)
\(684\) 2.75889 + 3.18393i 0.105489 + 0.121740i
\(685\) −3.43576 2.20803i −0.131274 0.0843644i
\(686\) −24.7010 + 28.5065i −0.943090 + 1.08838i
\(687\) 8.90815 2.61567i 0.339867 0.0997940i
\(688\) 1.78319 + 3.90465i 0.0679836 + 0.148863i
\(689\) 62.2371 2.37105
\(690\) −4.32341 2.07560i −0.164589 0.0790167i
\(691\) −3.43481 −0.130666 −0.0653331 0.997864i \(-0.520811\pi\)
−0.0653331 + 0.997864i \(0.520811\pi\)
\(692\) 4.37809 + 9.58667i 0.166430 + 0.364431i
\(693\) −6.46318 + 1.89776i −0.245516 + 0.0720899i
\(694\) −11.2004 + 12.9260i −0.425162 + 0.490663i
\(695\) −3.68250 2.36660i −0.139685 0.0897703i
\(696\) 2.01362 + 2.32384i 0.0763259 + 0.0880848i
\(697\) 1.43660 + 9.99178i 0.0544151 + 0.378465i
\(698\) 9.11425 + 2.67619i 0.344980 + 0.101295i
\(699\) −19.7787 + 12.7110i −0.748098 + 0.480774i
\(700\) −0.668052 + 4.64640i −0.0252500 + 0.175618i
\(701\) 0.627306 1.37361i 0.0236930 0.0518805i −0.897416 0.441186i \(-0.854558\pi\)
0.921109 + 0.389306i \(0.127285\pi\)
\(702\) 1.92403 4.21304i 0.0726179 0.159011i
\(703\) −6.87051 + 47.7854i −0.259126 + 1.80226i
\(704\) 1.20718 0.775805i 0.0454972 0.0292393i
\(705\) 0.283153 + 0.0831412i 0.0106642 + 0.00313128i
\(706\) −0.619954 4.31188i −0.0233323 0.162280i
\(707\) 7.03096 + 8.11416i 0.264427 + 0.305165i
\(708\) 12.3844 + 7.95895i 0.465433 + 0.299116i
\(709\) 27.6768 31.9407i 1.03942 1.19956i 0.0599056 0.998204i \(-0.480920\pi\)
0.979518 0.201355i \(-0.0645345\pi\)
\(710\) −11.4868 + 3.37283i −0.431092 + 0.126580i
\(711\) 5.70631 + 12.4951i 0.214003 + 0.468602i
\(712\) 5.56278 0.208474
\(713\) −36.2193 + 30.1871i −1.35642 + 1.13052i
\(714\) 15.5224 0.580911
\(715\) −2.76094 6.04561i −0.103253 0.226093i
\(716\) −13.1672 + 3.86625i −0.492083 + 0.144489i
\(717\) 1.61559 1.86448i 0.0603351 0.0696305i
\(718\) −11.3677 7.30559i −0.424240 0.272642i
\(719\) 14.1604 + 16.3420i 0.528094 + 0.609453i 0.955639 0.294541i \(-0.0951669\pi\)
−0.427545 + 0.903994i \(0.640621\pi\)
\(720\) −0.142315 0.989821i −0.00530376 0.0368885i
\(721\) 0.487278 + 0.143078i 0.0181472 + 0.00532849i
\(722\) −1.05254 + 0.676426i −0.0391715 + 0.0251740i
\(723\) −0.951958 + 6.62102i −0.0354037 + 0.246238i
\(724\) 2.63208 5.76344i 0.0978203 0.214197i
\(725\) 1.27735 2.79701i 0.0474396 0.103878i
\(726\) −1.27242 + 8.84985i −0.0472238 + 0.328449i
\(727\) −30.6873 + 19.7215i −1.13813 + 0.731432i −0.967241 0.253859i \(-0.918300\pi\)
−0.170888 + 0.985290i \(0.554664\pi\)
\(728\) 20.8609 + 6.12530i 0.773155 + 0.227019i
\(729\) −0.142315 0.989821i −0.00527092 0.0366601i
\(730\) 5.60463 + 6.46809i 0.207437 + 0.239395i
\(731\) −11.9410 7.67403i −0.441655 0.283834i
\(732\) −5.54836 + 6.40315i −0.205073 + 0.236667i
\(733\) 10.9310 3.20963i 0.403745 0.118550i −0.0735539 0.997291i \(-0.523434\pi\)
0.477299 + 0.878741i \(0.341616\pi\)
\(734\) 9.06846 + 19.8572i 0.334723 + 0.732941i
\(735\) −15.0354 −0.554588
\(736\) −0.0920206 + 4.79495i −0.00339192 + 0.176744i
\(737\) −17.0635 −0.628541
\(738\) 1.26815 + 2.77685i 0.0466811 + 0.102217i
\(739\) −6.66856 + 1.95806i −0.245307 + 0.0720286i −0.402075 0.915607i \(-0.631711\pi\)
0.156768 + 0.987635i \(0.449893\pi\)
\(740\) 7.50417 8.66027i 0.275859 0.318358i
\(741\) −16.4150 10.5493i −0.603022 0.387539i
\(742\) 41.3074 + 47.6713i 1.51644 + 1.75007i
\(743\) −3.07917 21.4161i −0.112964 0.785679i −0.965010 0.262213i \(-0.915548\pi\)
0.852046 0.523466i \(-0.175361\pi\)
\(744\) −9.43317 2.76983i −0.345837 0.101547i
\(745\) −12.7942 + 8.22235i −0.468744 + 0.301244i
\(746\) −0.842529 + 5.85992i −0.0308472 + 0.214547i
\(747\) 3.88436 8.50557i 0.142121 0.311203i
\(748\) −1.97117 + 4.31627i −0.0720732 + 0.157818i
\(749\) 8.11591 56.4474i 0.296549 2.06254i
\(750\) −0.841254 + 0.540641i −0.0307182 + 0.0197414i
\(751\) −43.3952 12.7420i −1.58351 0.464962i −0.632616 0.774466i \(-0.718019\pi\)
−0.950898 + 0.309504i \(0.899837\pi\)
\(752\) −0.0419981 0.292103i −0.00153151 0.0106519i
\(753\) −6.34289 7.32008i −0.231148 0.266759i
\(754\) −11.9808 7.69957i −0.436314 0.280402i
\(755\) 7.12394 8.22146i 0.259267 0.299210i
\(756\) 4.50404 1.32250i 0.163810 0.0480990i
\(757\) 14.9031 + 32.6332i 0.541662 + 1.18607i 0.960568 + 0.278044i \(0.0896862\pi\)
−0.418907 + 0.908029i \(0.637587\pi\)
\(758\) 13.4209 0.487469
\(759\) 5.11356 + 4.60565i 0.185610 + 0.167174i
\(760\) −4.21294 −0.152819
\(761\) 9.81389 + 21.4894i 0.355753 + 0.778991i 0.999901 + 0.0140895i \(0.00448499\pi\)
−0.644148 + 0.764901i \(0.722788\pi\)
\(762\) −7.99399 + 2.34725i −0.289592 + 0.0850318i
\(763\) −2.59139 + 2.99063i −0.0938147 + 0.108268i
\(764\) 10.9334 + 7.02650i 0.395558 + 0.254210i
\(765\) 2.16545 + 2.49906i 0.0782919 + 0.0903537i
\(766\) 2.91490 + 20.2736i 0.105319 + 0.732513i
\(767\) −65.4213 19.2094i −2.36223 0.693612i
\(768\) −0.841254 + 0.540641i −0.0303561 + 0.0195087i
\(769\) 2.57692 17.9229i 0.0929262 0.646316i −0.889120 0.457675i \(-0.848682\pi\)
0.982046 0.188642i \(-0.0604084\pi\)
\(770\) 2.79825 6.12731i 0.100842 0.220813i
\(771\) −0.621552 + 1.36101i −0.0223847 + 0.0490156i
\(772\) 1.27272 8.85196i 0.0458062 0.318589i
\(773\) −25.0497 + 16.0984i −0.900974 + 0.579021i −0.907079 0.420960i \(-0.861693\pi\)
0.00610491 + 0.999981i \(0.498057\pi\)
\(774\) −4.11868 1.20935i −0.148043 0.0434693i
\(775\) 1.39916 + 9.73134i 0.0502592 + 0.349560i
\(776\) 6.75242 + 7.79271i 0.242398 + 0.279742i
\(777\) 45.2523 + 29.0819i 1.62342 + 1.04331i
\(778\) −8.09444 + 9.34148i −0.290200 + 0.334908i
\(779\) 12.3400 3.62334i 0.442125 0.129820i
\(780\) 1.92403 + 4.21304i 0.0688914 + 0.150851i
\(781\) 17.1791 0.614717
\(782\) −8.31620 13.5031i −0.297387 0.482869i
\(783\) −3.07488 −0.109887
\(784\) 6.24592 + 13.6767i 0.223069 + 0.488452i
\(785\) −14.9809 + 4.39880i −0.534692 + 0.157000i
\(786\) −10.3026 + 11.8898i −0.367482 + 0.424097i
\(787\) −35.7068 22.9474i −1.27281 0.817986i −0.282828 0.959171i \(-0.591273\pi\)
−0.989983 + 0.141185i \(0.954909\pi\)
\(788\) 6.96651 + 8.03978i 0.248172 + 0.286405i
\(789\) 2.76936 + 19.2614i 0.0985920 + 0.685722i
\(790\) −13.1800 3.86999i −0.468923 0.137688i
\(791\) −49.4088 + 31.7531i −1.75677 + 1.12901i
\(792\) −0.204218 + 1.42037i −0.00725657 + 0.0504706i
\(793\) 16.3015 35.6953i 0.578884 1.26758i
\(794\) 1.75793 3.84934i 0.0623867 0.136608i
\(795\) −1.91236 + 13.3007i −0.0678244 + 0.471729i
\(796\) 21.3844 13.7429i 0.757951 0.487106i
\(797\) 15.4850 + 4.54680i 0.548506 + 0.161056i 0.544232 0.838935i \(-0.316821\pi\)
0.00427432 + 0.999991i \(0.498639\pi\)
\(798\) −2.81446 19.5750i −0.0996309 0.692948i
\(799\) 0.639038 + 0.737489i 0.0226075 + 0.0260905i
\(800\) 0.841254 + 0.540641i 0.0297428 + 0.0191145i
\(801\) −3.64285 + 4.20407i −0.128714 + 0.148543i
\(802\) −27.7786 + 8.15653i −0.980896 + 0.288017i
\(803\) −5.10181 11.1714i −0.180039 0.394230i
\(804\) 11.8911 0.419368
\(805\) 11.8056 + 19.1688i 0.416091 + 0.675611i
\(806\) 45.5351 1.60391
\(807\) 13.5336 + 29.6345i 0.476406 + 1.04318i
\(808\) 2.19456 0.644381i 0.0772043 0.0226692i
\(809\) 6.89705 7.95962i 0.242487 0.279845i −0.621440 0.783462i \(-0.713452\pi\)
0.863927 + 0.503616i \(0.167997\pi\)
\(810\) 0.841254 + 0.540641i 0.0295586 + 0.0189962i
\(811\) −34.7224 40.0718i −1.21927 1.40711i −0.885618 0.464414i \(-0.846265\pi\)
−0.333650 0.942697i \(-0.608280\pi\)
\(812\) −2.05418 14.2871i −0.0720875 0.501380i
\(813\) 21.6343 + 6.35241i 0.758748 + 0.222789i
\(814\) −13.8333 + 8.89010i −0.484856 + 0.311598i
\(815\) −1.42869 + 9.93673i −0.0500447 + 0.348068i
\(816\) 1.37367 3.00791i 0.0480879 0.105298i
\(817\) −7.51248 + 16.4500i −0.262828 + 0.575514i
\(818\) −1.82450 + 12.6897i −0.0637921 + 0.443684i
\(819\) −18.2902 + 11.7544i −0.639110 + 0.410731i
\(820\) −2.92906 0.860051i −0.102287 0.0300343i
\(821\) −6.26233 43.5555i −0.218557 1.52010i −0.743371 0.668880i \(-0.766774\pi\)
0.524814 0.851217i \(-0.324135\pi\)
\(822\) −2.67451 3.08655i −0.0932844 0.107656i
\(823\) 3.38554 + 2.17575i 0.118012 + 0.0758420i 0.598316 0.801261i \(-0.295837\pi\)
−0.480303 + 0.877103i \(0.659473\pi\)
\(824\) 0.0708473 0.0817622i 0.00246808 0.00284832i
\(825\) 1.37685 0.404279i 0.0479357 0.0140752i
\(826\) −28.7071 62.8598i −0.998848 2.18717i
\(827\) −19.5779 −0.680792 −0.340396 0.940282i \(-0.610561\pi\)
−0.340396 + 0.940282i \(0.610561\pi\)
\(828\) −3.56352 3.20957i −0.123841 0.111540i
\(829\) −8.55886 −0.297262 −0.148631 0.988893i \(-0.547487\pi\)
−0.148631 + 0.988893i \(0.547487\pi\)
\(830\) 3.88436 + 8.50557i 0.134828 + 0.295233i
\(831\) 12.1463 3.56648i 0.421351 0.123720i
\(832\) 3.03305 3.50032i 0.105152 0.121352i
\(833\) −41.8254 26.8795i −1.44916 0.931321i
\(834\) −2.86659 3.30822i −0.0992618 0.114554i
\(835\) −1.59559 11.0976i −0.0552176 0.384047i
\(836\) 5.80057 + 1.70320i 0.200617 + 0.0589065i
\(837\) 8.27071 5.31526i 0.285878 0.183722i
\(838\) 0.336876 2.34302i 0.0116372 0.0809383i
\(839\) −5.63295 + 12.3344i −0.194471 + 0.425832i −0.981598 0.190959i \(-0.938840\pi\)
0.787127 + 0.616791i \(0.211568\pi\)
\(840\) −1.95003 + 4.26998i −0.0672826 + 0.147328i
\(841\) 2.78156 19.3462i 0.0959160 0.667110i
\(842\) 20.5141 13.1836i 0.706961 0.454336i
\(843\) 8.78258 + 2.57880i 0.302488 + 0.0888185i
\(844\) 0.557472 + 3.87731i 0.0191890 + 0.133462i
\(845\) −5.53465 6.38732i −0.190398 0.219731i
\(846\) 0.248260 + 0.159547i 0.00853534 + 0.00548533i
\(847\) 27.4845 31.7188i 0.944379 1.08987i
\(848\) 12.8932 3.78579i 0.442755 0.130004i
\(849\) 1.17887 + 2.58137i 0.0404588 + 0.0885925i
\(850\) −3.30673 −0.113420
\(851\) 1.05448 54.9462i 0.0361471 1.88353i
\(852\) −11.9717 −0.410145
\(853\) −7.88984 17.2763i −0.270143 0.591531i 0.725134 0.688608i \(-0.241778\pi\)
−0.995277 + 0.0970772i \(0.969051\pi\)
\(854\) 38.1608 11.2050i 1.30584 0.383428i
\(855\) 2.75889 3.18393i 0.0943520 0.108888i
\(856\) −10.2201 6.56803i −0.349315 0.224491i
\(857\) 9.81979 + 11.3326i 0.335438 + 0.387116i 0.898262 0.439461i \(-0.144831\pi\)
−0.562824 + 0.826577i \(0.690285\pi\)
\(858\) −0.945855 6.57856i −0.0322909 0.224588i
\(859\) −0.733496 0.215374i −0.0250266 0.00734846i 0.269195 0.963086i \(-0.413242\pi\)
−0.294222 + 0.955737i \(0.595060\pi\)
\(860\) 3.61113 2.32073i 0.123138 0.0791363i
\(861\) 2.03938 14.1842i 0.0695018 0.483395i
\(862\) 3.89691 8.53305i 0.132729 0.290637i
\(863\) 2.56099 5.60779i 0.0871772 0.190892i −0.861022 0.508568i \(-0.830175\pi\)
0.948199 + 0.317676i \(0.102902\pi\)
\(864\) 0.142315 0.989821i 0.00484165 0.0336744i
\(865\) 8.86603 5.69785i 0.301454 0.193733i
\(866\) 12.3377 + 3.62267i 0.419251 + 0.123103i
\(867\) −0.863216 6.00380i −0.0293164 0.203900i
\(868\) 30.2221 + 34.8782i 1.02581 + 1.18384i
\(869\) 16.5823 + 10.6568i 0.562515 + 0.361506i
\(870\) 2.01362 2.32384i 0.0682680 0.0787854i
\(871\) −52.8440 + 15.5164i −1.79055 + 0.525753i
\(872\) 0.350192 + 0.766814i 0.0118590 + 0.0259676i
\(873\) −10.3112 −0.348982
\(874\) −15.5206 + 12.9357i −0.524993 + 0.437558i
\(875\) 4.69418 0.158692
\(876\) 3.55533 + 7.78509i 0.120124 + 0.263034i
\(877\) 11.5733 3.39824i 0.390804 0.114750i −0.0804263 0.996761i \(-0.525628\pi\)
0.471231 + 0.882010i \(0.343810\pi\)
\(878\) 5.56993 6.42804i 0.187976 0.216936i
\(879\) −10.1653 6.53283i −0.342867 0.220347i
\(880\) −0.939708 1.08448i −0.0316775 0.0365578i
\(881\) 6.95765 + 48.3915i 0.234409 + 1.63035i 0.678663 + 0.734450i \(0.262560\pi\)
−0.444254 + 0.895901i \(0.646531\pi\)
\(882\) −14.4263 4.23595i −0.485760 0.142632i
\(883\) 40.6633 26.1327i 1.36843 0.879437i 0.369667 0.929164i \(-0.379472\pi\)
0.998763 + 0.0497276i \(0.0158353\pi\)
\(884\) −2.17961 + 15.1595i −0.0733083 + 0.509870i
\(885\) 6.11546 13.3910i 0.205569 0.450133i
\(886\) 3.20628 7.02078i 0.107717 0.235868i
\(887\) −6.54237 + 45.5032i −0.219671 + 1.52785i 0.519582 + 0.854421i \(0.326088\pi\)
−0.739253 + 0.673428i \(0.764821\pi\)
\(888\) 9.64008 6.19530i 0.323500 0.207901i
\(889\) 37.5253 + 11.0184i 1.25856 + 0.369546i
\(890\) −0.791666 5.50616i −0.0265367 0.184567i
\(891\) −0.939708 1.08448i −0.0314814 0.0363315i
\(892\) −13.4711 8.65732i −0.451044 0.289869i
\(893\) 0.814166 0.939598i 0.0272450 0.0314424i
\(894\) −14.5925 + 4.28474i −0.488046 + 0.143303i
\(895\) 5.70079 + 12.4830i 0.190556 + 0.417260i
\(896\) 4.69418 0.156822
\(897\) 20.0243 + 9.61332i 0.668591 + 0.320980i
\(898\) −28.0148 −0.934867
\(899\) −12.5582 27.4985i −0.418838 0.917127i
\(900\) −0.959493 + 0.281733i −0.0319831 + 0.00939109i
\(901\) −29.0983 + 33.5812i −0.969403 + 1.11875i
\(902\) 3.68517 + 2.36832i 0.122703 + 0.0788563i
\(903\) 13.1955 + 15.2284i 0.439118 + 0.506769i
\(904\) 1.78060 + 12.3844i 0.0592220 + 0.411898i
\(905\) −6.07936 1.78506i −0.202085 0.0593375i
\(906\) 9.15162 5.88139i 0.304042 0.195396i
\(907\) 1.99604 13.8828i 0.0662775 0.460970i −0.929474 0.368888i \(-0.879739\pi\)
0.995751 0.0920822i \(-0.0293523\pi\)
\(908\) −4.09463 + 8.96599i −0.135885 + 0.297547i
\(909\) −0.950141 + 2.08052i −0.0315142 + 0.0690064i
\(910\) 3.09414 21.5202i 0.102570 0.713389i
\(911\) 18.4675 11.8683i 0.611854 0.393215i −0.197698 0.980263i \(-0.563346\pi\)
0.809552 + 0.587048i \(0.199710\pi\)
\(912\) −4.04228 1.18692i −0.133853 0.0393029i
\(913\) −1.90955 13.2812i −0.0631970 0.439545i
\(914\) −8.45822 9.76131i −0.279773 0.322875i
\(915\) 7.12759 + 4.58062i 0.235631 + 0.151431i
\(916\) −6.07988 + 7.01655i −0.200885 + 0.231833i
\(917\) 70.8598 20.8063i 2.34000 0.687085i
\(918\) 1.37367 + 3.00791i 0.0453377 + 0.0992757i
\(919\) −54.3659 −1.79337 −0.896683 0.442673i \(-0.854030\pi\)
−0.896683 + 0.442673i \(0.854030\pi\)
\(920\) 4.75924 0.591308i 0.156907 0.0194949i
\(921\) 6.43046 0.211891
\(922\) −4.99113 10.9290i −0.164374 0.359929i
\(923\) 53.2021 15.6216i 1.75117 0.514190i
\(924\) 4.41116 5.09075i 0.145117 0.167473i
\(925\) −9.64008 6.19530i −0.316964 0.203700i
\(926\) −0.468715 0.540927i −0.0154029 0.0177759i
\(927\) 0.0153966 + 0.107086i 0.000505691 + 0.00351716i
\(928\) −2.95032 0.866293i −0.0968491 0.0284375i
\(929\) −8.75811 + 5.62850i −0.287344 + 0.184665i −0.676370 0.736562i \(-0.736448\pi\)
0.389026 + 0.921227i \(0.372812\pi\)
\(930\) −1.39916 + 9.73134i −0.0458801 + 0.319103i
\(931\) −26.3137 + 57.6189i −0.862396 + 1.88838i
\(932\) 9.76680 21.3863i 0.319922 0.700532i
\(933\) 0.761092 5.29351i 0.0249170 0.173302i
\(934\) −2.75691 + 1.77176i −0.0902088 + 0.0579736i
\(935\) 4.55286 + 1.33684i 0.148895 + 0.0437194i
\(936\) 0.659144 + 4.58445i 0.0215448 + 0.149847i
\(937\) −1.87210 2.16052i −0.0611588 0.0705810i 0.724346 0.689437i \(-0.242142\pi\)
−0.785505 + 0.618856i \(0.787596\pi\)
\(938\) −46.9581 30.1781i −1.53324 0.985352i
\(939\) 15.4242 17.8004i 0.503349 0.580895i
\(940\) −0.283153 + 0.0831412i −0.00923543 + 0.00271177i
\(941\) −0.525311 1.15027i −0.0171246 0.0374977i 0.900876 0.434076i \(-0.142925\pi\)
−0.918001 + 0.396578i \(0.870198\pi\)
\(942\) −15.6134 −0.508711
\(943\) −13.4316 + 5.82517i −0.437392 + 0.189694i
\(944\) −14.7213 −0.479138
\(945\) −1.95003 4.26998i −0.0634346 0.138902i
\(946\) −5.91019 + 1.73539i −0.192157 + 0.0564224i
\(947\) 37.1522 42.8759i 1.20728 1.39328i 0.310639 0.950528i \(-0.399457\pi\)
0.896645 0.442751i \(-0.145997\pi\)
\(948\) −11.5558 7.42646i −0.375315 0.241200i
\(949\) −25.9584 29.9575i −0.842644 0.972463i
\(950\) 0.599564 + 4.17006i 0.0194524 + 0.135294i
\(951\) −11.1321 3.26869i −0.360984 0.105995i
\(952\) −13.0583 + 8.39204i −0.423221 + 0.271988i
\(953\) 2.93928 20.4431i 0.0952126 0.662218i −0.885192 0.465225i \(-0.845973\pi\)
0.980405 0.196993i \(-0.0631176\pi\)
\(954\) −5.58215 + 12.2232i −0.180729 + 0.395741i
\(955\) 5.39899 11.8221i 0.174707 0.382555i
\(956\) −0.351100 + 2.44196i −0.0113554 + 0.0789785i
\(957\) −3.71192 + 2.38551i −0.119989 + 0.0771124i
\(958\) 12.0507 + 3.53841i 0.389341 + 0.114321i
\(959\) 2.72839 + 18.9764i 0.0881043 + 0.612779i
\(960\) 0.654861 + 0.755750i 0.0211355 + 0.0243917i
\(961\) 55.2339 + 35.4967i 1.78174 + 1.14505i
\(962\) −34.7562 + 40.1108i −1.12059 + 1.29323i
\(963\) 11.6565 3.42266i 0.375626 0.110294i
\(964\) −2.77875 6.08462i −0.0894976 0.195972i
\(965\) −8.94299 −0.287885
\(966\) 5.92688 + 21.7183i 0.190694 + 0.698776i
\(967\) −43.0077 −1.38303 −0.691517 0.722360i \(-0.743057\pi\)
−0.691517 + 0.722360i \(0.743057\pi\)
\(968\) −3.71416 8.13288i −0.119378 0.261401i
\(969\) 13.3667 3.92483i 0.429402 0.126084i
\(970\) 6.75242 7.79271i 0.216807 0.250209i
\(971\) −8.01856 5.15322i −0.257328 0.165375i 0.405616 0.914043i \(-0.367057\pi\)
−0.662944 + 0.748669i \(0.730693\pi\)
\(972\) 0.654861 + 0.755750i 0.0210047 + 0.0242407i
\(973\) 2.92433 + 20.3392i 0.0937497 + 0.652044i
\(974\) −1.04575 0.307059i −0.0335079 0.00983881i
\(975\) 3.89634 2.50403i 0.124783 0.0801931i
\(976\) 1.20577 8.38634i 0.0385959 0.268440i
\(977\) −12.6895 + 27.7862i −0.405974 + 0.888959i 0.590656 + 0.806924i \(0.298869\pi\)
−0.996629 + 0.0820351i \(0.973858\pi\)
\(978\) −4.17031 + 9.13171i −0.133352 + 0.292000i
\(979\) −1.13602 + 7.90120i −0.0363074 + 0.252523i
\(980\) 12.6486 8.12874i 0.404043 0.259663i
\(981\) −0.808846 0.237499i −0.0258245 0.00758275i
\(982\) 2.39958 + 16.6895i 0.0765738 + 0.532582i
\(983\) −37.2175 42.9513i −1.18706 1.36993i −0.912866 0.408259i \(-0.866136\pi\)
−0.274189 0.961676i \(-0.588409\pi\)
\(984\) −2.56811 1.65043i −0.0818684 0.0526136i
\(985\) 6.96651 8.03978i 0.221971 0.256169i
\(986\) 9.75592 2.86460i 0.310692 0.0912273i
\(987\) −0.575468 1.26010i −0.0183174 0.0401094i
\(988\) 19.5126 0.620779
\(989\) 6.17779 19.6376i 0.196442 0.624438i
\(990\) 1.43497 0.0456065
\(991\) 1.07583 + 2.35575i 0.0341750 + 0.0748328i 0.925950 0.377647i \(-0.123267\pi\)
−0.891775 + 0.452480i \(0.850539\pi\)
\(992\) 9.43317 2.76983i 0.299503 0.0879422i
\(993\) 12.9236 14.9146i 0.410117 0.473301i
\(994\) 47.2764 + 30.3827i 1.49952 + 0.963680i
\(995\) −16.6464 19.2109i −0.527726 0.609028i
\(996\) 1.33072 + 9.25539i 0.0421656 + 0.293268i
\(997\) 30.4012 + 8.92659i 0.962815 + 0.282708i 0.725113 0.688630i \(-0.241788\pi\)
0.237702 + 0.971338i \(0.423606\pi\)
\(998\) 33.6394 21.6187i 1.06484 0.684329i
\(999\) −1.63081 + 11.3425i −0.0515966 + 0.358862i
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 690.2.m.c.211.1 yes 20
23.6 even 11 inner 690.2.m.c.121.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.c.121.1 20 23.6 even 11 inner
690.2.m.c.211.1 yes 20 1.1 even 1 trivial