Properties

Label 845.2.w.a.116.23
Level $845$
Weight $2$
Character 845.116
Analytic conductor $6.747$
Analytic rank $0$
Dimension $744$
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] = [845,2,Mod(51,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.51");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.w (of order \(26\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(744\)
Relative dimension: \(62\) over \(\Q(\zeta_{26})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label 116.23
Character \(\chi\) \(=\) 845.116
Dual form 845.2.w.a.51.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.611111 - 0.689802i) q^{2} +(1.09930 + 2.89862i) q^{3} +(0.138704 - 1.14233i) q^{4} +(0.239316 + 0.970942i) q^{5} +(1.32768 - 2.52968i) q^{6} +(3.88346 - 2.68056i) q^{7} +(-2.38961 + 1.64943i) q^{8} +(-4.94801 + 4.38355i) q^{9} +O(q^{10})\) \(q+(-0.611111 - 0.689802i) q^{2} +(1.09930 + 2.89862i) q^{3} +(0.138704 - 1.14233i) q^{4} +(0.239316 + 0.970942i) q^{5} +(1.32768 - 2.52968i) q^{6} +(3.88346 - 2.68056i) q^{7} +(-2.38961 + 1.64943i) q^{8} +(-4.94801 + 4.38355i) q^{9} +(0.523509 - 0.758433i) q^{10} +(-2.44383 + 2.75852i) q^{11} +(3.46365 - 0.853713i) q^{12} +(-3.60318 + 0.130784i) q^{13} +(-4.22227 - 1.04070i) q^{14} +(-2.55131 + 1.76104i) q^{15} +(0.363536 + 0.0896035i) q^{16} +(3.10375 + 4.49656i) q^{17} +(6.04756 + 0.734307i) q^{18} +4.10193i q^{19} +(1.14233 - 0.138704i) q^{20} +(12.0390 + 8.30993i) q^{21} +3.39628 q^{22} +6.89762 q^{23} +(-7.40797 - 5.11335i) q^{24} +(-0.885456 + 0.464723i) q^{25} +(2.29216 + 2.40555i) q^{26} +(-9.91068 - 5.20152i) q^{27} +(-2.52342 - 4.80798i) q^{28} +(0.549339 - 0.486672i) q^{29} +(2.77391 + 0.683706i) q^{30} +(-2.49070 + 4.74564i) q^{31} +(2.53838 + 4.83648i) q^{32} +(-10.6824 - 4.05130i) q^{33} +(1.20500 - 4.88887i) q^{34} +(3.53204 + 3.12911i) q^{35} +(4.32115 + 6.26026i) q^{36} +(-0.151962 + 0.289539i) q^{37} +(2.82952 - 2.50673i) q^{38} +(-4.34008 - 10.3005i) q^{39} +(-2.17337 - 1.92544i) q^{40} +(8.86300 - 3.36129i) q^{41} +(-1.62497 - 13.3828i) q^{42} +(1.10164 - 0.578187i) q^{43} +(2.81216 + 3.17427i) q^{44} +(-5.44031 - 3.75518i) q^{45} +(-4.21521 - 4.75799i) q^{46} +(-3.99008 + 0.484483i) q^{47} +(0.139909 + 1.15225i) q^{48} +(5.41362 - 14.2745i) q^{49} +(0.861679 + 0.326792i) q^{50} +(-9.62187 + 13.9397i) q^{51} +(-0.350376 + 4.13415i) q^{52} +(0.318542 + 0.461488i) q^{53} +(2.46850 + 10.0151i) q^{54} +(-3.26321 - 1.71266i) q^{55} +(-4.85856 + 12.8110i) q^{56} +(-11.8899 + 4.50926i) q^{57} +(-0.671415 - 0.0815245i) q^{58} +(2.25218 + 9.13746i) q^{59} +(1.65781 + 3.15870i) q^{60} +(5.75199 - 8.33319i) q^{61} +(4.79565 - 1.18202i) q^{62} +(-7.46501 + 30.2868i) q^{63} +(2.05052 - 5.40677i) q^{64} +(-0.989281 - 3.46718i) q^{65} +(3.73354 + 9.84454i) q^{66} +(-3.67100 + 0.445740i) q^{67} +(5.56705 - 2.92181i) q^{68} +(7.58257 + 19.9936i) q^{69} -4.34864i q^{70} +(9.37006 - 3.55359i) q^{71} +(4.59345 - 18.6364i) q^{72} +(-7.40634 + 8.36003i) q^{73} +(0.292590 - 0.0721169i) q^{74} +(-2.32044 - 2.05573i) q^{75} +(4.68574 + 0.568952i) q^{76} +(-2.09616 + 17.2634i) q^{77} +(-4.45302 + 9.28853i) q^{78} +(-0.798874 - 6.57932i) q^{79} +0.374415i q^{80} +(1.79201 - 14.7585i) q^{81} +(-7.73490 - 4.05959i) q^{82} +(-16.5282 - 6.26831i) q^{83} +(11.1625 - 12.5999i) q^{84} +(-3.62312 + 4.08966i) q^{85} +(-1.07206 - 0.406579i) q^{86} +(2.01457 + 1.05733i) q^{87} +(1.28983 - 10.6227i) q^{88} +5.15280i q^{89} +(0.734307 + 6.04756i) q^{90} +(-13.6422 + 10.1664i) q^{91} +(0.956725 - 7.87934i) q^{92} +(-16.4938 - 2.00272i) q^{93} +(2.77258 + 2.45629i) q^{94} +(-3.98273 + 0.981656i) q^{95} +(-11.2287 + 12.6746i) q^{96} +(3.18694 - 12.9299i) q^{97} +(-13.1549 + 4.98900i) q^{98} -24.3618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9} - 2 q^{10} - 122 q^{13} - 4 q^{14} - 66 q^{16} - 12 q^{17} - 78 q^{18} - 24 q^{22} + 140 q^{23} + 156 q^{24} + 62 q^{25} - 14 q^{26} + 28 q^{27} + 8 q^{29} - 20 q^{30} - 52 q^{31} - 26 q^{32} - 130 q^{34} + 4 q^{35} + 70 q^{36} + 126 q^{38} + 16 q^{39} + 6 q^{40} - 24 q^{42} - 24 q^{43} - 78 q^{47} - 94 q^{48} - 32 q^{49} - 12 q^{51} + 110 q^{52} - 156 q^{54} + 16 q^{55} + 16 q^{56} - 78 q^{57} - 104 q^{58} - 104 q^{59} + 28 q^{61} + 106 q^{62} + 14 q^{64} - 2 q^{65} - 308 q^{66} - 104 q^{67} - 18 q^{68} + 20 q^{69} - 78 q^{71} - 338 q^{72} - 4 q^{75} - 286 q^{76} - 52 q^{77} + 312 q^{78} - 12 q^{79} - 78 q^{81} + 268 q^{82} + 12 q^{87} - 72 q^{88} + 26 q^{90} - 136 q^{91} + 52 q^{92} - 130 q^{93} + 124 q^{94} - 16 q^{95} + 338 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{7}{26}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.611111 0.689802i −0.432121 0.487763i 0.491605 0.870818i \(-0.336410\pi\)
−0.923726 + 0.383055i \(0.874872\pi\)
\(3\) 1.09930 + 2.89862i 0.634682 + 1.67352i 0.734580 + 0.678522i \(0.237379\pi\)
−0.0998975 + 0.994998i \(0.531851\pi\)
\(4\) 0.138704 1.14233i 0.0693518 0.571164i
\(5\) 0.239316 + 0.970942i 0.107025 + 0.434218i
\(6\) 1.32768 2.52968i 0.542022 1.03274i
\(7\) 3.88346 2.68056i 1.46781 1.01316i 0.476850 0.878985i \(-0.341778\pi\)
0.990958 0.134170i \(-0.0428369\pi\)
\(8\) −2.38961 + 1.64943i −0.844854 + 0.583161i
\(9\) −4.94801 + 4.38355i −1.64934 + 1.46118i
\(10\) 0.523509 0.758433i 0.165548 0.239838i
\(11\) −2.44383 + 2.75852i −0.736843 + 0.831724i −0.990778 0.135497i \(-0.956737\pi\)
0.253934 + 0.967221i \(0.418275\pi\)
\(12\) 3.46365 0.853713i 0.999870 0.246446i
\(13\) −3.60318 + 0.130784i −0.999342 + 0.0362729i
\(14\) −4.22227 1.04070i −1.12845 0.278138i
\(15\) −2.55131 + 1.76104i −0.658746 + 0.454700i
\(16\) 0.363536 + 0.0896035i 0.0908839 + 0.0224009i
\(17\) 3.10375 + 4.49656i 0.752770 + 1.09058i 0.992797 + 0.119810i \(0.0382285\pi\)
−0.240026 + 0.970766i \(0.577156\pi\)
\(18\) 6.04756 + 0.734307i 1.42542 + 0.173078i
\(19\) 4.10193i 0.941047i 0.882387 + 0.470524i \(0.155935\pi\)
−0.882387 + 0.470524i \(0.844065\pi\)
\(20\) 1.14233 0.138704i 0.255432 0.0310151i
\(21\) 12.0390 + 8.30993i 2.62713 + 1.81338i
\(22\) 3.39628 0.724090
\(23\) 6.89762 1.43825 0.719127 0.694879i \(-0.244542\pi\)
0.719127 + 0.694879i \(0.244542\pi\)
\(24\) −7.40797 5.11335i −1.51215 1.04376i
\(25\) −0.885456 + 0.464723i −0.177091 + 0.0929446i
\(26\) 2.29216 + 2.40555i 0.449529 + 0.471768i
\(27\) −9.91068 5.20152i −1.90731 1.00103i
\(28\) −2.52342 4.80798i −0.476882 0.908623i
\(29\) 0.549339 0.486672i 0.102010 0.0903728i −0.610576 0.791957i \(-0.709062\pi\)
0.712586 + 0.701585i \(0.247524\pi\)
\(30\) 2.77391 + 0.683706i 0.506444 + 0.124827i
\(31\) −2.49070 + 4.74564i −0.447344 + 0.852342i 0.552479 + 0.833527i \(0.313682\pi\)
−0.999823 + 0.0188154i \(0.994011\pi\)
\(32\) 2.53838 + 4.83648i 0.448727 + 0.854977i
\(33\) −10.6824 4.05130i −1.85957 0.705241i
\(34\) 1.20500 4.88887i 0.206656 0.838434i
\(35\) 3.53204 + 3.12911i 0.597023 + 0.528916i
\(36\) 4.32115 + 6.26026i 0.720191 + 1.04338i
\(37\) −0.151962 + 0.289539i −0.0249824 + 0.0475999i −0.897627 0.440755i \(-0.854711\pi\)
0.872645 + 0.488355i \(0.162403\pi\)
\(38\) 2.82952 2.50673i 0.459008 0.406646i
\(39\) −4.34008 10.3005i −0.694968 1.64940i
\(40\) −2.17337 1.92544i −0.343640 0.304438i
\(41\) 8.86300 3.36129i 1.38417 0.524946i 0.453647 0.891182i \(-0.350123\pi\)
0.930522 + 0.366236i \(0.119354\pi\)
\(42\) −1.62497 13.3828i −0.250738 2.06501i
\(43\) 1.10164 0.578187i 0.167999 0.0881727i −0.378628 0.925549i \(-0.623604\pi\)
0.546627 + 0.837376i \(0.315912\pi\)
\(44\) 2.81216 + 3.17427i 0.423949 + 0.478540i
\(45\) −5.44031 3.75518i −0.810994 0.559789i
\(46\) −4.21521 4.75799i −0.621499 0.701527i
\(47\) −3.99008 + 0.484483i −0.582013 + 0.0706691i −0.406248 0.913763i \(-0.633163\pi\)
−0.175765 + 0.984432i \(0.556240\pi\)
\(48\) 0.139909 + 1.15225i 0.0201941 + 0.166313i
\(49\) 5.41362 14.2745i 0.773374 2.03922i
\(50\) 0.861679 + 0.326792i 0.121860 + 0.0462153i
\(51\) −9.62187 + 13.9397i −1.34733 + 1.95195i
\(52\) −0.350376 + 4.13415i −0.0485884 + 0.573303i
\(53\) 0.318542 + 0.461488i 0.0437551 + 0.0633902i 0.844251 0.535948i \(-0.180046\pi\)
−0.800496 + 0.599338i \(0.795430\pi\)
\(54\) 2.46850 + 10.0151i 0.335921 + 1.36288i
\(55\) −3.26321 1.71266i −0.440011 0.230935i
\(56\) −4.85856 + 12.8110i −0.649252 + 1.71194i
\(57\) −11.8899 + 4.50926i −1.57486 + 0.597266i
\(58\) −0.671415 0.0815245i −0.0881611 0.0107047i
\(59\) 2.25218 + 9.13746i 0.293209 + 1.18960i 0.914031 + 0.405644i \(0.132953\pi\)
−0.620822 + 0.783951i \(0.713201\pi\)
\(60\) 1.65781 + 3.15870i 0.214023 + 0.407786i
\(61\) 5.75199 8.33319i 0.736467 1.06696i −0.258427 0.966031i \(-0.583204\pi\)
0.994894 0.100925i \(-0.0321803\pi\)
\(62\) 4.79565 1.18202i 0.609048 0.150117i
\(63\) −7.46501 + 30.2868i −0.940503 + 3.81577i
\(64\) 2.05052 5.40677i 0.256315 0.675847i
\(65\) −0.989281 3.46718i −0.122705 0.430051i
\(66\) 3.73354 + 9.84454i 0.459567 + 1.21178i
\(67\) −3.67100 + 0.445740i −0.448484 + 0.0544558i −0.341663 0.939823i \(-0.610990\pi\)
−0.106821 + 0.994278i \(0.534067\pi\)
\(68\) 5.56705 2.92181i 0.675103 0.354322i
\(69\) 7.58257 + 19.9936i 0.912834 + 2.40695i
\(70\) 4.34864i 0.519762i
\(71\) 9.37006 3.55359i 1.11202 0.421734i 0.270915 0.962603i \(-0.412674\pi\)
0.841107 + 0.540869i \(0.181905\pi\)
\(72\) 4.59345 18.6364i 0.541344 2.19632i
\(73\) −7.40634 + 8.36003i −0.866846 + 0.978467i −0.999920 0.0126388i \(-0.995977\pi\)
0.133074 + 0.991106i \(0.457515\pi\)
\(74\) 0.292590 0.0721169i 0.0340129 0.00838342i
\(75\) −2.32044 2.05573i −0.267941 0.237375i
\(76\) 4.68574 + 0.568952i 0.537492 + 0.0652633i
\(77\) −2.09616 + 17.2634i −0.238879 + 1.96735i
\(78\) −4.45302 + 9.28853i −0.504205 + 1.05172i
\(79\) −0.798874 6.57932i −0.0898803 0.740231i −0.966073 0.258270i \(-0.916848\pi\)
0.876193 0.481961i \(-0.160075\pi\)
\(80\) 0.374415i 0.0418609i
\(81\) 1.79201 14.7585i 0.199112 1.63984i
\(82\) −7.73490 4.05959i −0.854177 0.448307i
\(83\) −16.5282 6.26831i −1.81420 0.688037i −0.993102 0.117255i \(-0.962590\pi\)
−0.821102 0.570781i \(-0.806640\pi\)
\(84\) 11.1625 12.5999i 1.21793 1.37476i
\(85\) −3.62312 + 4.08966i −0.392983 + 0.443586i
\(86\) −1.07206 0.406579i −0.115603 0.0438426i
\(87\) 2.01457 + 1.05733i 0.215984 + 0.113357i
\(88\) 1.28983 10.6227i 0.137496 1.13238i
\(89\) 5.15280i 0.546196i 0.961986 + 0.273098i \(0.0880483\pi\)
−0.961986 + 0.273098i \(0.911952\pi\)
\(90\) 0.734307 + 6.04756i 0.0774028 + 0.637469i
\(91\) −13.6422 + 10.1664i −1.43009 + 1.06573i
\(92\) 0.956725 7.87934i 0.0997455 0.821478i
\(93\) −16.4938 2.00272i −1.71033 0.207672i
\(94\) 2.77258 + 2.45629i 0.285970 + 0.253347i
\(95\) −3.98273 + 0.981656i −0.408620 + 0.100716i
\(96\) −11.2287 + 12.6746i −1.14602 + 1.29359i
\(97\) 3.18694 12.9299i 0.323585 1.31284i −0.553639 0.832757i \(-0.686761\pi\)
0.877225 0.480080i \(-0.159392\pi\)
\(98\) −13.1549 + 4.98900i −1.32885 + 0.503965i
\(99\) 24.3618i 2.44846i
\(100\) 0.408050 + 1.07594i 0.0408050 + 0.107594i
\(101\) −1.30700 + 0.685965i −0.130051 + 0.0682561i −0.528494 0.848937i \(-0.677243\pi\)
0.398443 + 0.917193i \(0.369551\pi\)
\(102\) 15.4956 1.88151i 1.53430 0.186297i
\(103\) 3.39752 + 8.95851i 0.334767 + 0.882708i 0.991678 + 0.128740i \(0.0410934\pi\)
−0.656911 + 0.753968i \(0.728137\pi\)
\(104\) 8.39447 6.25571i 0.823146 0.613423i
\(105\) −5.18733 + 13.6779i −0.506232 + 1.33482i
\(106\) 0.123671 0.501751i 0.0120119 0.0487344i
\(107\) 0.881438 0.217255i 0.0852118 0.0210028i −0.196479 0.980508i \(-0.562951\pi\)
0.281691 + 0.959505i \(0.409105\pi\)
\(108\) −7.31649 + 10.5998i −0.704030 + 1.01996i
\(109\) −3.24513 6.18307i −0.310827 0.592231i 0.679061 0.734082i \(-0.262387\pi\)
−0.989888 + 0.141851i \(0.954695\pi\)
\(110\) 0.812784 + 3.29759i 0.0774959 + 0.314413i
\(111\) −1.00632 0.122189i −0.0955152 0.0115976i
\(112\) 1.65196 0.626506i 0.156096 0.0591993i
\(113\) 6.49199 17.1180i 0.610715 1.61032i −0.170007 0.985443i \(-0.554379\pi\)
0.780721 0.624879i \(-0.214852\pi\)
\(114\) 10.3766 + 5.44604i 0.971854 + 0.510069i
\(115\) 1.65071 + 6.69719i 0.153929 + 0.624516i
\(116\) −0.479744 0.695029i −0.0445431 0.0645318i
\(117\) 17.2553 16.4418i 1.59525 1.52005i
\(118\) 4.92670 7.13756i 0.453540 0.657065i
\(119\) 24.1066 + 9.14242i 2.20985 + 0.838084i
\(120\) 3.19192 8.41641i 0.291382 0.768310i
\(121\) −0.311194 2.56291i −0.0282904 0.232992i
\(122\) −9.26335 + 1.12477i −0.838665 + 0.101832i
\(123\) 19.4862 + 21.9954i 1.75702 + 1.98326i
\(124\) 5.07560 + 3.50344i 0.455803 + 0.314618i
\(125\) −0.663123 0.748511i −0.0593115 0.0669488i
\(126\) 25.4538 13.3592i 2.26761 1.19013i
\(127\) 0.438785 + 3.61372i 0.0389358 + 0.320666i 0.999144 + 0.0413786i \(0.0131750\pi\)
−0.960208 + 0.279287i \(0.909902\pi\)
\(128\) 5.23167 1.98411i 0.462419 0.175372i
\(129\) 2.88699 + 2.55765i 0.254185 + 0.225188i
\(130\) −1.78710 + 2.80124i −0.156739 + 0.245685i
\(131\) −0.835085 + 0.739820i −0.0729617 + 0.0646384i −0.698815 0.715302i \(-0.746289\pi\)
0.625854 + 0.779940i \(0.284751\pi\)
\(132\) −6.10960 + 11.6409i −0.531773 + 1.01321i
\(133\) 10.9955 + 15.9297i 0.953427 + 1.38128i
\(134\) 2.55086 + 2.25986i 0.220361 + 0.195222i
\(135\) 2.67860 10.8675i 0.230537 0.935325i
\(136\) −14.8335 5.62561i −1.27196 0.482392i
\(137\) −8.54977 16.2902i −0.730456 1.39177i −0.912748 0.408523i \(-0.866044\pi\)
0.182292 0.983244i \(-0.441648\pi\)
\(138\) 9.15782 17.4488i 0.779566 1.48534i
\(139\) −3.02252 0.744983i −0.256366 0.0631887i 0.109038 0.994038i \(-0.465223\pi\)
−0.365404 + 0.930849i \(0.619069\pi\)
\(140\) 4.06437 3.60072i 0.343502 0.304317i
\(141\) −5.79063 11.0331i −0.487659 0.929157i
\(142\) −8.17742 4.29184i −0.686234 0.360163i
\(143\) 8.44480 10.2590i 0.706189 0.857904i
\(144\) −2.19156 + 1.15022i −0.182630 + 0.0958516i
\(145\) 0.603996 + 0.416908i 0.0501591 + 0.0346224i
\(146\) 10.2929 0.851843
\(147\) 47.3277 3.90352
\(148\) 0.309670 + 0.213750i 0.0254548 + 0.0175701i
\(149\) −19.4626 + 2.36318i −1.59443 + 0.193599i −0.869043 0.494737i \(-0.835264\pi\)
−0.725392 + 0.688336i \(0.758341\pi\)
\(150\) 2.85692i 0.233267i
\(151\) −2.73451 0.332029i −0.222531 0.0270201i 0.00851169 0.999964i \(-0.497291\pi\)
−0.231043 + 0.972944i \(0.574214\pi\)
\(152\) −6.76584 9.80201i −0.548782 0.795048i
\(153\) −35.0683 8.64356i −2.83510 0.698791i
\(154\) 13.1893 9.10393i 1.06283 0.733615i
\(155\) −5.20380 1.28262i −0.417980 0.103023i
\(156\) −12.3685 + 3.52907i −0.990273 + 0.282552i
\(157\) 3.27219 0.806522i 0.261149 0.0643675i −0.106567 0.994306i \(-0.533986\pi\)
0.367716 + 0.929938i \(0.380140\pi\)
\(158\) −4.05022 + 4.57176i −0.322218 + 0.363709i
\(159\) −0.987504 + 1.43065i −0.0783142 + 0.113458i
\(160\) −4.08847 + 3.62207i −0.323222 + 0.286349i
\(161\) 26.7866 18.4895i 2.11108 1.45717i
\(162\) −11.2756 + 7.78297i −0.885893 + 0.611488i
\(163\) 7.87087 14.9967i 0.616494 1.17463i −0.354393 0.935097i \(-0.615313\pi\)
0.970888 0.239535i \(-0.0769951\pi\)
\(164\) −2.61037 10.5907i −0.203835 0.826993i
\(165\) 1.37711 11.3415i 0.107208 0.882937i
\(166\) 5.77666 + 15.2318i 0.448356 + 1.18222i
\(167\) 3.18052 + 3.59007i 0.246116 + 0.277808i 0.858568 0.512700i \(-0.171355\pi\)
−0.612451 + 0.790508i \(0.709816\pi\)
\(168\) −42.4752 −3.27703
\(169\) 12.9658 0.942476i 0.997369 0.0724981i
\(170\) 5.03518 0.386181
\(171\) −17.9810 20.2964i −1.37504 1.55210i
\(172\) −0.507677 1.33863i −0.0387100 0.102070i
\(173\) −0.285382 + 2.35034i −0.0216972 + 0.178693i −0.999529 0.0307011i \(-0.990226\pi\)
0.977831 + 0.209394i \(0.0671491\pi\)
\(174\) −0.501779 2.03580i −0.0380398 0.154333i
\(175\) −2.19291 + 4.17825i −0.165769 + 0.315846i
\(176\) −1.13559 + 0.783843i −0.0855985 + 0.0590844i
\(177\) −24.0102 + 16.5730i −1.80472 + 1.24571i
\(178\) 3.55441 3.14893i 0.266414 0.236022i
\(179\) 9.91793 14.3686i 0.741301 1.07396i −0.253012 0.967463i \(-0.581421\pi\)
0.994313 0.106497i \(-0.0339634\pi\)
\(180\) −5.04423 + 5.69376i −0.375975 + 0.424388i
\(181\) 22.8341 5.62811i 1.69725 0.418334i 0.732344 0.680935i \(-0.238426\pi\)
0.964905 + 0.262601i \(0.0845803\pi\)
\(182\) 15.3497 + 3.19761i 1.13780 + 0.237023i
\(183\) 30.4779 + 7.51214i 2.25299 + 0.555313i
\(184\) −16.4826 + 11.3771i −1.21512 + 0.838733i
\(185\) −0.317492 0.0782548i −0.0233425 0.00575341i
\(186\) 8.69809 + 12.6014i 0.637775 + 0.923977i
\(187\) −19.9889 2.42709i −1.46173 0.177486i
\(188\) 4.62517i 0.337325i
\(189\) −52.4307 + 6.36623i −3.81377 + 0.463075i
\(190\) 3.11104 + 2.14740i 0.225699 + 0.155788i
\(191\) 8.31773 0.601850 0.300925 0.953648i \(-0.402705\pi\)
0.300925 + 0.953648i \(0.402705\pi\)
\(192\) 17.9263 1.29372
\(193\) −2.88581 1.99193i −0.207725 0.143382i 0.459660 0.888095i \(-0.347971\pi\)
−0.667385 + 0.744713i \(0.732587\pi\)
\(194\) −10.8667 + 5.70327i −0.780182 + 0.409471i
\(195\) 8.96252 6.67903i 0.641819 0.478295i
\(196\) −15.5553 8.16405i −1.11109 0.583146i
\(197\) −4.39816 8.38000i −0.313356 0.597050i 0.676938 0.736040i \(-0.263307\pi\)
−0.990294 + 0.138990i \(0.955614\pi\)
\(198\) −16.8048 + 14.8878i −1.19427 + 1.05803i
\(199\) 5.91354 + 1.45756i 0.419200 + 0.103323i 0.443273 0.896387i \(-0.353817\pi\)
−0.0240730 + 0.999710i \(0.507663\pi\)
\(200\) 1.34937 2.57100i 0.0954146 0.181797i
\(201\) −5.32757 10.1508i −0.375777 0.715984i
\(202\) 1.27190 + 0.482368i 0.0894906 + 0.0339393i
\(203\) 0.828783 3.36251i 0.0581692 0.236002i
\(204\) 14.5891 + 12.9248i 1.02144 + 0.904917i
\(205\) 5.38468 + 7.80105i 0.376082 + 0.544849i
\(206\) 4.10334 7.81826i 0.285893 0.544724i
\(207\) −34.1295 + 30.2361i −2.37216 + 2.10155i
\(208\) −1.32160 0.275313i −0.0916366 0.0190895i
\(209\) −11.3152 10.0244i −0.782692 0.693404i
\(210\) 12.6051 4.78047i 0.869831 0.329884i
\(211\) −1.38976 11.4457i −0.0956747 0.787952i −0.959020 0.283338i \(-0.908558\pi\)
0.863345 0.504614i \(-0.168365\pi\)
\(212\) 0.571353 0.299869i 0.0392407 0.0205951i
\(213\) 20.6010 + 23.2538i 1.41156 + 1.59332i
\(214\) −0.688519 0.475250i −0.0470662 0.0324875i
\(215\) 0.825027 + 0.931263i 0.0562664 + 0.0635116i
\(216\) 32.2622 3.91734i 2.19516 0.266541i
\(217\) 3.04841 + 25.1060i 0.206940 + 1.70430i
\(218\) −2.28196 + 6.01704i −0.154554 + 0.407525i
\(219\) −32.3744 12.2780i −2.18766 0.829669i
\(220\) −2.40904 + 3.49010i −0.162417 + 0.235302i
\(221\) −11.7715 15.7960i −0.791833 1.06255i
\(222\) 0.530684 + 0.768829i 0.0356172 + 0.0516004i
\(223\) −4.91284 19.9322i −0.328988 1.33476i −0.869713 0.493558i \(-0.835696\pi\)
0.540725 0.841200i \(-0.318150\pi\)
\(224\) 22.8221 + 11.9780i 1.52487 + 0.800313i
\(225\) 2.34411 6.18090i 0.156274 0.412060i
\(226\) −15.7753 + 5.98279i −1.04936 + 0.397969i
\(227\) −7.06102 0.857363i −0.468656 0.0569052i −0.117198 0.993109i \(-0.537391\pi\)
−0.351459 + 0.936203i \(0.614314\pi\)
\(228\) 3.50187 + 14.2077i 0.231917 + 0.940925i
\(229\) 3.84880 + 7.33327i 0.254336 + 0.484596i 0.978827 0.204687i \(-0.0656177\pi\)
−0.724492 + 0.689284i \(0.757925\pi\)
\(230\) 3.61097 5.23139i 0.238100 0.344947i
\(231\) −52.3444 + 12.9017i −3.44401 + 0.848872i
\(232\) −0.509976 + 2.06905i −0.0334815 + 0.135840i
\(233\) −7.35929 + 19.4049i −0.482123 + 1.27125i 0.444674 + 0.895693i \(0.353320\pi\)
−0.926797 + 0.375562i \(0.877450\pi\)
\(234\) −21.8865 1.85492i −1.43076 0.121260i
\(235\) −1.42529 3.75819i −0.0929759 0.245157i
\(236\) 10.7504 1.30533i 0.699788 0.0849697i
\(237\) 18.1927 9.54829i 1.18175 0.620228i
\(238\) −8.42533 22.2158i −0.546133 1.44004i
\(239\) 12.9376i 0.836863i 0.908248 + 0.418432i \(0.137420\pi\)
−0.908248 + 0.418432i \(0.862580\pi\)
\(240\) −1.08529 + 0.411596i −0.0700551 + 0.0265684i
\(241\) 1.12739 4.57399i 0.0726214 0.294637i −0.923390 0.383863i \(-0.874593\pi\)
0.996011 + 0.0892266i \(0.0284395\pi\)
\(242\) −1.57773 + 1.78089i −0.101420 + 0.114480i
\(243\) 12.1469 2.99393i 0.779221 0.192061i
\(244\) −8.72141 7.72650i −0.558331 0.494638i
\(245\) 15.1553 + 1.84019i 0.968237 + 0.117565i
\(246\) 3.26422 26.8833i 0.208119 1.71402i
\(247\) −0.536466 14.7800i −0.0341345 0.940428i
\(248\) −1.87578 15.4485i −0.119112 0.980978i
\(249\) 54.7997i 3.47279i
\(250\) −0.111082 + 0.914846i −0.00702547 + 0.0578600i
\(251\) −4.69027 2.46164i −0.296047 0.155378i 0.310160 0.950684i \(-0.399617\pi\)
−0.606207 + 0.795307i \(0.707310\pi\)
\(252\) 33.5620 + 12.7284i 2.11420 + 0.801812i
\(253\) −16.8566 + 19.0272i −1.05977 + 1.19623i
\(254\) 2.22460 2.51106i 0.139584 0.157558i
\(255\) −15.8373 6.00629i −0.991769 0.376128i
\(256\) −14.8062 7.77087i −0.925385 0.485679i
\(257\) 0.371750 3.06163i 0.0231891 0.190979i −0.976511 0.215467i \(-0.930872\pi\)
0.999700 + 0.0244880i \(0.00779556\pi\)
\(258\) 3.55445i 0.221291i
\(259\) 0.185989 + 1.53175i 0.0115568 + 0.0951785i
\(260\) −4.09787 + 0.649172i −0.254139 + 0.0402599i
\(261\) −0.584783 + 4.81612i −0.0361971 + 0.298110i
\(262\) 1.02066 + 0.123930i 0.0630565 + 0.00765645i
\(263\) −4.56567 4.04483i −0.281531 0.249415i 0.510525 0.859863i \(-0.329451\pi\)
−0.792056 + 0.610448i \(0.790989\pi\)
\(264\) 32.2091 7.93883i 1.98233 0.488601i
\(265\) −0.371846 + 0.419727i −0.0228423 + 0.0257836i
\(266\) 4.26887 17.3195i 0.261741 1.06192i
\(267\) −14.9360 + 5.66448i −0.914069 + 0.346661i
\(268\) 4.25531i 0.259934i
\(269\) 9.98702 + 26.3336i 0.608919 + 1.60559i 0.783810 + 0.621001i \(0.213274\pi\)
−0.174890 + 0.984588i \(0.555957\pi\)
\(270\) −9.13334 + 4.79355i −0.555837 + 0.291726i
\(271\) 30.6379 3.72012i 1.86112 0.225981i 0.888582 0.458717i \(-0.151691\pi\)
0.972540 + 0.232736i \(0.0747679\pi\)
\(272\) 0.725417 + 1.91277i 0.0439849 + 0.115979i
\(273\) −44.4655 28.3676i −2.69117 1.71689i
\(274\) −6.01216 + 15.8528i −0.363208 + 0.957701i
\(275\) 0.881960 3.57825i 0.0531842 0.215777i
\(276\) 23.8910 5.88859i 1.43807 0.354452i
\(277\) −10.9489 + 15.8622i −0.657856 + 0.953069i 0.342055 + 0.939680i \(0.388877\pi\)
−0.999910 + 0.0133886i \(0.995738\pi\)
\(278\) 1.33320 + 2.54020i 0.0799601 + 0.152351i
\(279\) −8.47874 34.3996i −0.507609 2.05945i
\(280\) −13.6014 1.65151i −0.812841 0.0986968i
\(281\) −5.65998 + 2.14655i −0.337646 + 0.128052i −0.517600 0.855623i \(-0.673174\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(282\) −4.07195 + 10.7369i −0.242481 + 0.639370i
\(283\) 14.8320 + 7.78446i 0.881673 + 0.462738i 0.843870 0.536547i \(-0.180272\pi\)
0.0378031 + 0.999285i \(0.487964\pi\)
\(284\) −2.75971 11.1966i −0.163758 0.664394i
\(285\) −7.22368 10.4653i −0.427894 0.619911i
\(286\) −12.2374 + 0.444179i −0.723613 + 0.0262649i
\(287\) 25.4090 36.8112i 1.49984 2.17290i
\(288\) −33.7609 12.8038i −1.98938 0.754473i
\(289\) −4.55750 + 12.0171i −0.268088 + 0.706891i
\(290\) −0.0815245 0.671415i −0.00478728 0.0394268i
\(291\) 40.9824 4.97617i 2.40243 0.291708i
\(292\) 8.52260 + 9.62003i 0.498748 + 0.562970i
\(293\) 11.6897 + 8.06881i 0.682919 + 0.471385i 0.858322 0.513112i \(-0.171507\pi\)
−0.175403 + 0.984497i \(0.556123\pi\)
\(294\) −28.9224 32.6467i −1.68679 1.90399i
\(295\) −8.33296 + 4.37347i −0.485164 + 0.254633i
\(296\) −0.114444 0.942535i −0.00665195 0.0547837i
\(297\) 38.5685 14.6271i 2.23797 0.848751i
\(298\) 13.5239 + 11.9811i 0.783419 + 0.694048i
\(299\) −24.8534 + 0.902098i −1.43731 + 0.0521697i
\(300\) −2.67017 + 2.36556i −0.154162 + 0.136576i
\(301\) 2.72832 5.19838i 0.157258 0.299630i
\(302\) 1.44205 + 2.08917i 0.0829808 + 0.120218i
\(303\) −3.42514 3.03441i −0.196769 0.174322i
\(304\) −0.367547 + 1.49120i −0.0210803 + 0.0855260i
\(305\) 9.46759 + 3.59058i 0.542112 + 0.205596i
\(306\) 15.4683 + 29.4724i 0.884263 + 1.68482i
\(307\) 14.3116 27.2686i 0.816809 1.55630i −0.0141067 0.999900i \(-0.504490\pi\)
0.830915 0.556399i \(-0.187817\pi\)
\(308\) 19.4297 + 4.78900i 1.10711 + 0.272878i
\(309\) −22.2324 + 19.6962i −1.26476 + 1.12048i
\(310\) 2.29535 + 4.37342i 0.130367 + 0.248393i
\(311\) −7.32635 3.84516i −0.415439 0.218039i 0.244035 0.969766i \(-0.421529\pi\)
−0.659474 + 0.751727i \(0.729221\pi\)
\(312\) 27.3610 + 17.4555i 1.54901 + 0.988222i
\(313\) −0.715661 + 0.375608i −0.0404515 + 0.0212306i −0.484828 0.874610i \(-0.661118\pi\)
0.444376 + 0.895840i \(0.353425\pi\)
\(314\) −2.55601 1.76429i −0.144244 0.0995645i
\(315\) −31.1932 −1.75754
\(316\) −7.62654 −0.429026
\(317\) 6.09633 + 4.20799i 0.342404 + 0.236344i 0.726839 0.686808i \(-0.240988\pi\)
−0.384435 + 0.923152i \(0.625604\pi\)
\(318\) 1.59034 0.193102i 0.0891817 0.0108286i
\(319\) 2.70471i 0.151435i
\(320\) 5.74038 + 0.697009i 0.320897 + 0.0389640i
\(321\) 1.59871 + 2.31613i 0.0892311 + 0.129274i
\(322\) −29.1237 7.17834i −1.62300 0.400033i
\(323\) −18.4446 + 12.7314i −1.02628 + 0.708392i
\(324\) −16.6105 4.09412i −0.922806 0.227451i
\(325\) 3.12968 1.79028i 0.173603 0.0993071i
\(326\) −15.1547 + 3.73530i −0.839342 + 0.206879i
\(327\) 14.3550 16.2035i 0.793834 0.896053i
\(328\) −15.6349 + 22.6511i −0.863293 + 1.25070i
\(329\) −14.1966 + 12.5771i −0.782684 + 0.693398i
\(330\) −8.66498 + 5.98100i −0.476991 + 0.329243i
\(331\) 17.0259 11.7522i 0.935830 0.645957i 0.000601072 1.00000i \(-0.499809\pi\)
0.935229 + 0.354043i \(0.115193\pi\)
\(332\) −9.45298 + 18.0112i −0.518800 + 0.988491i
\(333\) −0.517301 2.09877i −0.0283479 0.115012i
\(334\) 0.532783 4.38786i 0.0291526 0.240093i
\(335\) −1.31131 3.45765i −0.0716448 0.188912i
\(336\) 3.63201 + 4.09969i 0.198142 + 0.223657i
\(337\) 0.0472941 0.00257627 0.00128814 0.999999i \(-0.499590\pi\)
0.00128814 + 0.999999i \(0.499590\pi\)
\(338\) −8.57366 8.36787i −0.466345 0.455152i
\(339\) 56.7551 3.08252
\(340\) 4.16919 + 4.70604i 0.226106 + 0.255221i
\(341\) −7.00406 18.4682i −0.379291 1.00011i
\(342\) −3.01208 + 24.8067i −0.162874 + 1.34139i
\(343\) −9.33525 37.8746i −0.504056 2.04504i
\(344\) −1.67882 + 3.19872i −0.0905159 + 0.172464i
\(345\) −17.5980 + 12.1470i −0.947444 + 0.653973i
\(346\) 1.79567 1.23946i 0.0965356 0.0666337i
\(347\) 10.5084 9.30961i 0.564119 0.499766i −0.332180 0.943216i \(-0.607784\pi\)
0.896299 + 0.443450i \(0.146246\pi\)
\(348\) 1.48724 2.15464i 0.0797245 0.115501i
\(349\) 0.702406 0.792853i 0.0375990 0.0424404i −0.729410 0.684076i \(-0.760205\pi\)
0.767009 + 0.641636i \(0.221744\pi\)
\(350\) 4.22227 1.04070i 0.225690 0.0556276i
\(351\) 36.3902 + 17.4459i 1.94237 + 0.931191i
\(352\) −19.5449 4.81738i −1.04175 0.256767i
\(353\) 4.05972 2.80222i 0.216077 0.149147i −0.455110 0.890435i \(-0.650400\pi\)
0.671187 + 0.741288i \(0.265785\pi\)
\(354\) 26.1050 + 6.43431i 1.38747 + 0.341980i
\(355\) 5.69273 + 8.24735i 0.302139 + 0.437724i
\(356\) 5.88618 + 0.714712i 0.311967 + 0.0378797i
\(357\) 79.9261i 4.23014i
\(358\) −15.9724 + 1.93941i −0.844170 + 0.102501i
\(359\) 24.2980 + 16.7717i 1.28240 + 0.885175i 0.997308 0.0733262i \(-0.0233614\pi\)
0.285089 + 0.958501i \(0.407977\pi\)
\(360\) 19.1941 1.01162
\(361\) 2.17418 0.114430
\(362\) −17.8365 12.3116i −0.937464 0.647085i
\(363\) 7.08682 3.71945i 0.371962 0.195220i
\(364\) 9.72115 + 16.9940i 0.509527 + 0.890727i
\(365\) −9.88955 5.19044i −0.517643 0.271680i
\(366\) −13.4435 25.6145i −0.702704 1.33889i
\(367\) −8.49059 + 7.52200i −0.443205 + 0.392645i −0.854997 0.518632i \(-0.826441\pi\)
0.411792 + 0.911278i \(0.364903\pi\)
\(368\) 2.50753 + 0.618051i 0.130714 + 0.0322181i
\(369\) −29.1198 + 55.4832i −1.51592 + 2.88834i
\(370\) 0.140043 + 0.266829i 0.00728047 + 0.0138718i
\(371\) 2.47409 + 0.938298i 0.128448 + 0.0487140i
\(372\) −4.57551 + 18.5636i −0.237229 + 0.962477i
\(373\) −16.0237 14.1957i −0.829674 0.735027i 0.137128 0.990553i \(-0.456213\pi\)
−0.966802 + 0.255526i \(0.917751\pi\)
\(374\) 10.5412 + 15.2716i 0.545073 + 0.789675i
\(375\) 1.44068 2.74498i 0.0743963 0.141750i
\(376\) 8.73561 7.73907i 0.450505 0.399112i
\(377\) −1.91572 + 1.82541i −0.0986646 + 0.0940135i
\(378\) 36.4324 + 32.2763i 1.87388 + 1.66011i
\(379\) −13.2023 + 5.00696i −0.678155 + 0.257190i −0.669544 0.742772i \(-0.733510\pi\)
−0.00861153 + 0.999963i \(0.502741\pi\)
\(380\) 0.568952 + 4.68574i 0.0291866 + 0.240374i
\(381\) −9.99244 + 5.24444i −0.511928 + 0.268681i
\(382\) −5.08306 5.73759i −0.260072 0.293560i
\(383\) 31.3346 + 21.6287i 1.60112 + 1.10517i 0.932260 + 0.361788i \(0.117833\pi\)
0.668862 + 0.743387i \(0.266782\pi\)
\(384\) 11.5024 + 12.9835i 0.586979 + 0.662562i
\(385\) −17.2634 + 2.09616i −0.879825 + 0.106830i
\(386\) 0.389512 + 3.20792i 0.0198257 + 0.163279i
\(387\) −2.91643 + 7.68999i −0.148250 + 0.390904i
\(388\) −14.3282 5.43396i −0.727403 0.275868i
\(389\) 1.12617 1.63154i 0.0570991 0.0827224i −0.793394 0.608708i \(-0.791688\pi\)
0.850493 + 0.525986i \(0.176303\pi\)
\(390\) −10.0843 2.10073i −0.510638 0.106375i
\(391\) 21.4085 + 31.0156i 1.08267 + 1.56853i
\(392\) 10.6084 + 43.0399i 0.535805 + 2.17384i
\(393\) −3.06247 1.60731i −0.154481 0.0810780i
\(394\) −3.09277 + 8.15497i −0.155812 + 0.410841i
\(395\) 6.19695 2.35019i 0.311802 0.118251i
\(396\) −27.8292 3.37908i −1.39847 0.169805i
\(397\) 1.32923 + 5.39288i 0.0667120 + 0.270661i 0.994820 0.101649i \(-0.0324119\pi\)
−0.928108 + 0.372310i \(0.878566\pi\)
\(398\) −2.60840 4.96990i −0.130748 0.249119i
\(399\) −34.0867 + 49.3832i −1.70647 + 2.47225i
\(400\) −0.363536 + 0.0896035i −0.0181768 + 0.00448017i
\(401\) −6.40082 + 25.9692i −0.319642 + 1.29684i 0.562869 + 0.826546i \(0.309698\pi\)
−0.882511 + 0.470292i \(0.844149\pi\)
\(402\) −3.74632 + 9.87824i −0.186850 + 0.492682i
\(403\) 8.35380 17.4251i 0.416132 0.868008i
\(404\) 0.602311 + 1.58816i 0.0299661 + 0.0790141i
\(405\) 14.7585 1.79201i 0.733357 0.0890457i
\(406\) −2.82594 + 1.48317i −0.140249 + 0.0736084i
\(407\) −0.427329 1.12677i −0.0211819 0.0558521i
\(408\) 49.1810i 2.43482i
\(409\) 17.1486 6.50362i 0.847945 0.321583i 0.107918 0.994160i \(-0.465582\pi\)
0.740028 + 0.672577i \(0.234812\pi\)
\(410\) 2.09054 8.48167i 0.103245 0.418880i
\(411\) 37.8204 42.6904i 1.86554 2.10576i
\(412\) 10.7048 2.63850i 0.527388 0.129989i
\(413\) 33.2397 + 29.4478i 1.63562 + 1.44903i
\(414\) 41.7138 + 5.06497i 2.05012 + 0.248930i
\(415\) 2.13071 17.5480i 0.104593 0.861398i
\(416\) −9.77877 17.0947i −0.479444 0.838138i
\(417\) −1.16323 9.58009i −0.0569638 0.469139i
\(418\) 13.9313i 0.681403i
\(419\) −3.07722 + 25.3432i −0.150332 + 1.23810i 0.700882 + 0.713278i \(0.252790\pi\)
−0.851214 + 0.524819i \(0.824133\pi\)
\(420\) 14.9051 + 7.82280i 0.727295 + 0.381714i
\(421\) −6.88613 2.61156i −0.335609 0.127280i 0.181043 0.983475i \(-0.442053\pi\)
−0.516652 + 0.856195i \(0.672822\pi\)
\(422\) −7.04594 + 7.95323i −0.342991 + 0.387157i
\(423\) 17.6192 19.8879i 0.856674 0.966985i
\(424\) −1.52238 0.577363i −0.0739334 0.0280392i
\(425\) −4.83789 2.53912i −0.234672 0.123165i
\(426\) 3.45097 28.4213i 0.167200 1.37702i
\(427\) 47.7801i 2.31224i
\(428\) −0.125918 1.03702i −0.00608646 0.0501265i
\(429\) 39.0205 + 13.2005i 1.88393 + 0.637325i
\(430\) 0.138204 1.13821i 0.00666477 0.0548893i
\(431\) −10.7638 1.30696i −0.518474 0.0629542i −0.142883 0.989740i \(-0.545637\pi\)
−0.375591 + 0.926785i \(0.622560\pi\)
\(432\) −3.13681 2.77897i −0.150920 0.133703i
\(433\) 7.34101 1.80940i 0.352786 0.0869540i −0.0589401 0.998262i \(-0.518772\pi\)
0.411726 + 0.911308i \(0.364926\pi\)
\(434\) 15.4552 17.4453i 0.741874 0.837402i
\(435\) −0.544485 + 2.20906i −0.0261061 + 0.105917i
\(436\) −7.51320 + 2.84938i −0.359817 + 0.136461i
\(437\) 28.2936i 1.35346i
\(438\) 11.3150 + 29.8351i 0.540650 + 1.42558i
\(439\) 28.5056 14.9609i 1.36050 0.714045i 0.382756 0.923849i \(-0.374975\pi\)
0.977743 + 0.209804i \(0.0672826\pi\)
\(440\) 10.6227 1.28983i 0.506418 0.0614902i
\(441\) 35.7866 + 94.3614i 1.70412 + 4.49340i
\(442\) −3.70244 + 17.7731i −0.176107 + 0.845379i
\(443\) −1.34121 + 3.53647i −0.0637226 + 0.168023i −0.963096 0.269159i \(-0.913254\pi\)
0.899373 + 0.437182i \(0.144023\pi\)
\(444\) −0.279159 + 1.13259i −0.0132483 + 0.0537505i
\(445\) −5.00307 + 1.23315i −0.237168 + 0.0584567i
\(446\) −10.7470 + 15.5697i −0.508883 + 0.737245i
\(447\) −28.2452 53.8167i −1.33595 2.54544i
\(448\) −6.53006 26.4935i −0.308516 1.25170i
\(449\) −6.46096 0.784502i −0.304911 0.0370230i −0.0333490 0.999444i \(-0.510617\pi\)
−0.271562 + 0.962421i \(0.587540\pi\)
\(450\) −5.69610 + 2.16025i −0.268517 + 0.101835i
\(451\) −12.3875 + 32.6632i −0.583305 + 1.53805i
\(452\) −18.6538 9.79029i −0.877403 0.460497i
\(453\) −2.04362 8.29130i −0.0960177 0.389559i
\(454\) 3.72366 + 5.39465i 0.174760 + 0.253183i
\(455\) −13.1358 10.8128i −0.615816 0.506912i
\(456\) 20.9746 30.3870i 0.982226 1.42300i
\(457\) −27.4492 10.4101i −1.28402 0.486964i −0.384208 0.923247i \(-0.625525\pi\)
−0.899810 + 0.436283i \(0.856295\pi\)
\(458\) 2.70646 7.13635i 0.126465 0.333460i
\(459\) −7.37131 60.7082i −0.344063 2.83362i
\(460\) 7.87934 0.956725i 0.367376 0.0446075i
\(461\) −23.0361 26.0024i −1.07290 1.21105i −0.976457 0.215714i \(-0.930792\pi\)
−0.0964425 0.995339i \(-0.530746\pi\)
\(462\) 40.8879 + 28.2229i 1.90228 + 1.31305i
\(463\) −24.3463 27.4813i −1.13147 1.27717i −0.956222 0.292642i \(-0.905465\pi\)
−0.175249 0.984524i \(-0.556073\pi\)
\(464\) 0.243312 0.127700i 0.0112955 0.00592832i
\(465\) −2.00272 16.4938i −0.0928737 0.764884i
\(466\) 17.8828 6.78207i 0.828407 0.314173i
\(467\) 10.3865 + 9.20162i 0.480629 + 0.425800i 0.868331 0.495984i \(-0.165193\pi\)
−0.387702 + 0.921785i \(0.626731\pi\)
\(468\) −16.3886 21.9917i −0.757563 1.01657i
\(469\) −13.0613 + 11.5713i −0.603116 + 0.534314i
\(470\) −1.72139 + 3.27984i −0.0794019 + 0.151288i
\(471\) 5.93493 + 8.59823i 0.273467 + 0.396185i
\(472\) −20.4534 18.1201i −0.941445 0.834047i
\(473\) −1.09729 + 4.45190i −0.0504536 + 0.204698i
\(474\) −17.7042 6.71432i −0.813181 0.308399i
\(475\) −1.90626 3.63208i −0.0874653 0.166651i
\(476\) 13.7873 26.2695i 0.631940 1.20406i
\(477\) −3.59911 0.887100i −0.164792 0.0406175i
\(478\) 8.92437 7.90630i 0.408191 0.361626i
\(479\) 6.09192 + 11.6072i 0.278347 + 0.530346i 0.983990 0.178221i \(-0.0570343\pi\)
−0.705643 + 0.708567i \(0.749342\pi\)
\(480\) −14.9935 7.86917i −0.684355 0.359177i
\(481\) 0.509678 1.06313i 0.0232393 0.0484748i
\(482\) −3.84410 + 2.01754i −0.175094 + 0.0918965i
\(483\) 83.0405 + 57.3187i 3.77848 + 2.60809i
\(484\) −2.97085 −0.135039
\(485\) 13.3169 0.604690
\(486\) −9.48829 6.54930i −0.430398 0.297082i
\(487\) 1.44322 0.175239i 0.0653986 0.00794083i −0.0877719 0.996141i \(-0.527975\pi\)
0.153171 + 0.988200i \(0.451052\pi\)
\(488\) 29.4006i 1.33090i
\(489\) 52.1222 + 6.32878i 2.35705 + 0.286197i
\(490\) −7.99221 11.5787i −0.361051 0.523073i
\(491\) 10.4320 + 2.57127i 0.470791 + 0.116040i 0.467572 0.883955i \(-0.345129\pi\)
0.00321958 + 0.999995i \(0.498975\pi\)
\(492\) 27.8288 19.2088i 1.25462 0.866000i
\(493\) 3.89336 + 0.959628i 0.175348 + 0.0432195i
\(494\) −9.86741 + 9.40226i −0.443956 + 0.423028i
\(495\) 23.6539 5.83017i 1.06317 0.262047i
\(496\) −1.33069 + 1.50203i −0.0597495 + 0.0674433i
\(497\) 26.8626 38.9172i 1.20495 1.74567i
\(498\) −37.8009 + 33.4887i −1.69390 + 1.50066i
\(499\) −11.1706 + 7.71050i −0.500064 + 0.345170i −0.791246 0.611498i \(-0.790567\pi\)
0.291181 + 0.956668i \(0.405952\pi\)
\(500\) −0.947022 + 0.653682i −0.0423521 + 0.0292335i
\(501\) −6.90990 + 13.1657i −0.308711 + 0.588200i
\(502\) 1.16823 + 4.73969i 0.0521406 + 0.211543i
\(503\) 0.0909439 0.748990i 0.00405499 0.0333958i −0.990541 0.137218i \(-0.956184\pi\)
0.994596 + 0.103822i \(0.0331071\pi\)
\(504\) −32.1174 84.6865i −1.43062 3.77224i
\(505\) −0.978817 1.10486i −0.0435568 0.0491655i
\(506\) 23.4263 1.04142
\(507\) 16.9852 + 36.5469i 0.754339 + 1.62310i
\(508\) 4.18891 0.185853
\(509\) 19.1317 + 21.5953i 0.847999 + 0.957193i 0.999511 0.0312626i \(-0.00995281\pi\)
−0.151512 + 0.988455i \(0.548414\pi\)
\(510\) 5.53519 + 14.5951i 0.245102 + 0.646282i
\(511\) −6.35267 + 52.3189i −0.281025 + 2.31445i
\(512\) 1.00977 + 4.09680i 0.0446260 + 0.181055i
\(513\) 21.3363 40.6529i 0.942020 1.79487i
\(514\) −2.33910 + 1.61456i −0.103173 + 0.0712154i
\(515\) −7.88512 + 5.44270i −0.347460 + 0.239834i
\(516\) 3.32210 2.94313i 0.146247 0.129564i
\(517\) 8.41463 12.1907i 0.370075 0.536146i
\(518\) 0.942946 1.06437i 0.0414307 0.0467656i
\(519\) −7.12645 + 1.75651i −0.312817 + 0.0771024i
\(520\) 8.08286 + 6.65345i 0.354457 + 0.291773i
\(521\) −9.12459 2.24901i −0.399755 0.0985309i 0.0343121 0.999411i \(-0.489076\pi\)
−0.434068 + 0.900880i \(0.642922\pi\)
\(522\) 3.67953 2.53980i 0.161049 0.111164i
\(523\) −27.9829 6.89716i −1.22361 0.301592i −0.425973 0.904736i \(-0.640068\pi\)
−0.797632 + 0.603144i \(0.793914\pi\)
\(524\) 0.729288 + 1.05656i 0.0318591 + 0.0461558i
\(525\) −14.5218 1.76327i −0.633785 0.0769554i
\(526\) 5.62125i 0.245098i
\(527\) −29.0696 + 3.52969i −1.26629 + 0.153756i
\(528\) −3.52042 2.42997i −0.153207 0.105751i
\(529\) 24.5772 1.06857
\(530\) 0.516767 0.0224469
\(531\) −51.1983 35.3397i −2.22182 1.53361i
\(532\) 19.7220 10.3509i 0.855057 0.448768i
\(533\) −31.4954 + 13.2705i −1.36422 + 0.574808i
\(534\) 13.0349 + 6.84126i 0.564077 + 0.296050i
\(535\) 0.421884 + 0.803833i 0.0182396 + 0.0347527i
\(536\) 8.03703 7.12019i 0.347147 0.307545i
\(537\) 52.5520 + 12.9529i 2.26778 + 0.558959i
\(538\) 12.0618 22.9818i 0.520021 0.990817i
\(539\) 26.1466 + 49.8181i 1.12621 + 2.14582i
\(540\) −12.0427 4.56720i −0.518236 0.196541i
\(541\) −8.86445 + 35.9645i −0.381113 + 1.54623i 0.396826 + 0.917894i \(0.370112\pi\)
−0.777938 + 0.628341i \(0.783734\pi\)
\(542\) −21.2893 18.8607i −0.914455 0.810136i
\(543\) 41.4154 + 60.0005i 1.77730 + 2.57487i
\(544\) −13.8690 + 26.4252i −0.594630 + 1.13297i
\(545\) 5.22679 4.63053i 0.223891 0.198350i
\(546\) 7.60531 + 48.0082i 0.325477 + 2.05456i
\(547\) 9.22815 + 8.17542i 0.394567 + 0.349556i 0.836959 0.547266i \(-0.184331\pi\)
−0.442392 + 0.896822i \(0.645870\pi\)
\(548\) −19.7946 + 7.50712i −0.845585 + 0.320688i
\(549\) 8.06811 + 66.4469i 0.344339 + 2.83588i
\(550\) −3.00726 + 1.57833i −0.128230 + 0.0673003i
\(551\) 1.99629 + 2.25335i 0.0850450 + 0.0959960i
\(552\) −51.0974 35.2700i −2.17485 1.50119i
\(553\) −20.7386 23.4091i −0.881896 0.995455i
\(554\) 17.6328 2.14101i 0.749145 0.0909627i
\(555\) −0.122189 1.00632i −0.00518663 0.0427157i
\(556\) −1.27025 + 3.34937i −0.0538705 + 0.142045i
\(557\) −0.832791 0.315836i −0.0352865 0.0133824i 0.336899 0.941541i \(-0.390622\pi\)
−0.372185 + 0.928159i \(0.621391\pi\)
\(558\) −18.5474 + 26.8706i −0.785176 + 1.13752i
\(559\) −3.89380 + 2.22739i −0.164690 + 0.0942085i
\(560\) 1.00364 + 1.45403i 0.0424116 + 0.0614438i
\(561\) −14.9386 60.6083i −0.630709 2.55889i
\(562\) 4.93956 + 2.59248i 0.208363 + 0.109357i
\(563\) 4.73219 12.4778i 0.199438 0.525875i −0.797565 0.603232i \(-0.793879\pi\)
0.997003 + 0.0773577i \(0.0246483\pi\)
\(564\) −13.4066 + 5.08446i −0.564521 + 0.214095i
\(565\) 18.1742 + 2.20674i 0.764593 + 0.0928384i
\(566\) −3.69429 14.9883i −0.155283 0.630007i
\(567\) −32.6019 62.1177i −1.36915 2.60870i
\(568\) −16.5294 + 23.9469i −0.693557 + 1.00479i
\(569\) 13.7290 3.38390i 0.575550 0.141860i 0.0592124 0.998245i \(-0.481141\pi\)
0.516338 + 0.856385i \(0.327295\pi\)
\(570\) −2.80452 + 11.3784i −0.117468 + 0.476587i
\(571\) 7.69115 20.2799i 0.321865 0.848687i −0.672247 0.740327i \(-0.734671\pi\)
0.994112 0.108360i \(-0.0345600\pi\)
\(572\) −10.5479 11.0697i −0.441028 0.462847i
\(573\) 9.14370 + 24.1100i 0.381984 + 1.00721i
\(574\) −40.9201 + 4.96860i −1.70797 + 0.207385i
\(575\) −6.10754 + 3.20548i −0.254702 + 0.133678i
\(576\) 13.5549 + 35.7413i 0.564787 + 1.48922i
\(577\) 3.20307i 0.133346i 0.997775 + 0.0666729i \(0.0212384\pi\)
−0.997775 + 0.0666729i \(0.978762\pi\)
\(578\) 11.0746 4.20004i 0.460642 0.174698i
\(579\) 2.60147 10.5546i 0.108114 0.438634i
\(580\) 0.560022 0.632134i 0.0232537 0.0262479i
\(581\) −80.9890 + 19.9620i −3.35999 + 0.828164i
\(582\) −28.4774 25.2288i −1.18043 1.04577i
\(583\) −2.05149 0.249095i −0.0849638 0.0103165i
\(584\) 3.90899 32.1934i 0.161755 1.33217i
\(585\) 20.0935 + 12.8191i 0.830765 + 0.530003i
\(586\) −1.57782 12.9945i −0.0651791 0.536798i
\(587\) 7.13291i 0.294407i −0.989106 0.147203i \(-0.952973\pi\)
0.989106 0.147203i \(-0.0470272\pi\)
\(588\) 6.56452 54.0637i 0.270716 2.22955i
\(589\) −19.4663 10.2167i −0.802094 0.420971i
\(590\) 8.10919 + 3.07541i 0.333850 + 0.126613i
\(591\) 19.4555 21.9608i 0.800294 0.903345i
\(592\) −0.0811872 + 0.0916414i −0.00333677 + 0.00376644i
\(593\) −27.2187 10.3227i −1.11774 0.423902i −0.274579 0.961565i \(-0.588538\pi\)
−0.843160 + 0.537662i \(0.819308\pi\)
\(594\) −33.6595 17.6658i −1.38106 0.724839i
\(595\) −3.10767 + 25.5940i −0.127402 + 1.04925i
\(596\) 22.5604i 0.924109i
\(597\) 2.27586 + 18.7434i 0.0931449 + 0.767117i
\(598\) 15.8104 + 16.5926i 0.646537 + 0.678522i
\(599\) 3.54892 29.2280i 0.145005 1.19422i −0.720548 0.693405i \(-0.756110\pi\)
0.865553 0.500817i \(-0.166967\pi\)
\(600\) 8.93573 + 1.08499i 0.364799 + 0.0442947i
\(601\) −19.5439 17.3144i −0.797213 0.706269i 0.162667 0.986681i \(-0.447990\pi\)
−0.959880 + 0.280412i \(0.909529\pi\)
\(602\) −5.25316 + 1.29479i −0.214103 + 0.0527716i
\(603\) 16.2102 18.2975i 0.660130 0.745133i
\(604\) −0.758572 + 3.07765i −0.0308659 + 0.125228i
\(605\) 2.41397 0.915497i 0.0981417 0.0372202i
\(606\) 4.21703i 0.171305i
\(607\) −9.57572 25.2491i −0.388667 1.02483i −0.976437 0.215802i \(-0.930763\pi\)
0.587771 0.809028i \(-0.300006\pi\)
\(608\) −19.8389 + 10.4123i −0.804574 + 0.422273i
\(609\) 10.6577 1.29408i 0.431872 0.0524388i
\(610\) −3.30896 8.72500i −0.133976 0.353265i
\(611\) 14.3136 2.26752i 0.579066 0.0917339i
\(612\) −14.7379 + 38.8606i −0.595743 + 1.57085i
\(613\) −4.06549 + 16.4944i −0.164204 + 0.666201i 0.829914 + 0.557892i \(0.188390\pi\)
−0.994117 + 0.108309i \(0.965457\pi\)
\(614\) −27.5559 + 6.79192i −1.11207 + 0.274100i
\(615\) −16.6929 + 24.1839i −0.673123 + 0.975187i
\(616\) −23.4658 44.7103i −0.945462 1.80143i
\(617\) −1.45033 5.88422i −0.0583881 0.236890i 0.934496 0.355973i \(-0.115851\pi\)
−0.992884 + 0.119083i \(0.962004\pi\)
\(618\) 27.1730 + 3.29940i 1.09306 + 0.132721i
\(619\) −15.0838 + 5.72053i −0.606269 + 0.229928i −0.638586 0.769550i \(-0.720481\pi\)
0.0323173 + 0.999478i \(0.489711\pi\)
\(620\) −2.18696 + 5.76654i −0.0878305 + 0.231590i
\(621\) −68.3601 35.8782i −2.74320 1.43974i
\(622\) 1.82481 + 7.40355i 0.0731682 + 0.296855i
\(623\) 13.8124 + 20.0107i 0.553381 + 0.801711i
\(624\) −0.654813 4.13348i −0.0262135 0.165472i
\(625\) 0.568065 0.822984i 0.0227226 0.0329194i
\(626\) 0.696443 + 0.264126i 0.0278355 + 0.0105566i
\(627\) 16.6182 43.8185i 0.663665 1.74994i
\(628\) −0.467448 3.84978i −0.0186532 0.153623i
\(629\) −1.77358 + 0.215352i −0.0707173 + 0.00858663i
\(630\) 19.0625 + 21.5171i 0.759468 + 0.857262i
\(631\) −31.9370 22.0445i −1.27139 0.877577i −0.274915 0.961468i \(-0.588650\pi\)
−0.996475 + 0.0838913i \(0.973265\pi\)
\(632\) 12.7611 + 14.4043i 0.507610 + 0.572973i
\(633\) 31.6489 16.6106i 1.25793 0.660213i
\(634\) −0.822853 6.77681i −0.0326797 0.269141i
\(635\) −3.40370 + 1.29085i −0.135072 + 0.0512260i
\(636\) 1.49730 + 1.32649i 0.0593717 + 0.0525987i
\(637\) −17.6393 + 52.1417i −0.698896 + 2.06593i
\(638\) 1.86571 1.65288i 0.0738642 0.0654380i
\(639\) −30.7858 + 58.6574i −1.21787 + 2.32045i
\(640\) 3.17848 + 4.60482i 0.125640 + 0.182022i
\(641\) 18.3375 + 16.2456i 0.724286 + 0.641662i 0.942487 0.334242i \(-0.108480\pi\)
−0.218201 + 0.975904i \(0.570019\pi\)
\(642\) 0.620681 2.51820i 0.0244963 0.0993854i
\(643\) −8.28655 3.14267i −0.326789 0.123935i 0.185754 0.982596i \(-0.440527\pi\)
−0.512543 + 0.858661i \(0.671297\pi\)
\(644\) −17.4056 33.1636i −0.685877 1.30683i
\(645\) −1.79242 + 3.41518i −0.0705766 + 0.134473i
\(646\) 20.0538 + 4.94282i 0.789006 + 0.194473i
\(647\) −20.0969 + 17.8043i −0.790091 + 0.699960i −0.958291 0.285793i \(-0.907743\pi\)
0.168200 + 0.985753i \(0.446205\pi\)
\(648\) 20.0609 + 38.2229i 0.788068 + 1.50154i
\(649\) −30.7098 16.1177i −1.20546 0.632677i
\(650\) −3.14752 1.06479i −0.123456 0.0417647i
\(651\) −69.4215 + 36.4352i −2.72084 + 1.42801i
\(652\) −16.0394 11.0712i −0.628152 0.433582i
\(653\) −19.3793 −0.758372 −0.379186 0.925321i \(-0.623796\pi\)
−0.379186 + 0.925321i \(0.623796\pi\)
\(654\) −19.9497 −0.780094
\(655\) −0.918171 0.633768i −0.0358759 0.0247634i
\(656\) 3.52320 0.427794i 0.137558 0.0167026i
\(657\) 73.8316i 2.88044i
\(658\) 17.3514 + 2.10684i 0.676428 + 0.0821332i
\(659\) 17.9631 + 26.0241i 0.699744 + 1.01375i 0.998238 + 0.0593421i \(0.0189003\pi\)
−0.298494 + 0.954411i \(0.596484\pi\)
\(660\) −12.7647 3.14622i −0.496867 0.122467i
\(661\) −17.2152 + 11.8828i −0.669595 + 0.462188i −0.853732 0.520713i \(-0.825666\pi\)
0.184137 + 0.982901i \(0.441051\pi\)
\(662\) −18.5114 4.56265i −0.719466 0.177332i
\(663\) 32.8462 51.4855i 1.27564 1.99953i
\(664\) 49.8350 12.2832i 1.93397 0.476682i
\(665\) −12.8354 + 14.4882i −0.497735 + 0.561827i
\(666\) −1.13161 + 1.63942i −0.0438490 + 0.0635262i
\(667\) 3.78914 3.35688i 0.146716 0.129979i
\(668\) 4.54218 3.13524i 0.175742 0.121306i
\(669\) 52.3751 36.1520i 2.02494 1.39772i
\(670\) −1.58374 + 3.01756i −0.0611850 + 0.116578i
\(671\) 8.93036 + 36.2319i 0.344753 + 1.39872i
\(672\) −9.63122 + 79.3202i −0.371532 + 3.05984i
\(673\) −3.54668 9.35182i −0.136714 0.360486i 0.849122 0.528197i \(-0.177132\pi\)
−0.985836 + 0.167711i \(0.946362\pi\)
\(674\) −0.0289019 0.0326236i −0.00111326 0.00125661i
\(675\) 11.1927 0.430809
\(676\) 0.721787 14.9419i 0.0277610 0.574688i
\(677\) −36.4955 −1.40264 −0.701319 0.712848i \(-0.747405\pi\)
−0.701319 + 0.712848i \(0.747405\pi\)
\(678\) −34.6837 39.1498i −1.33202 1.50354i
\(679\) −22.2831 58.7557i −0.855146 2.25484i
\(680\) 1.91225 15.7488i 0.0733313 0.603938i
\(681\) −5.27703 21.4097i −0.202216 0.820423i
\(682\) −8.45913 + 16.1175i −0.323917 + 0.617172i
\(683\) 0.758354 0.523454i 0.0290176 0.0200294i −0.553468 0.832871i \(-0.686696\pi\)
0.582485 + 0.812841i \(0.302080\pi\)
\(684\) −25.6791 + 17.7250i −0.981867 + 0.677734i
\(685\) 13.7708 12.1998i 0.526154 0.466132i
\(686\) −20.4211 + 29.5850i −0.779680 + 1.12956i
\(687\) −17.0254 + 19.2177i −0.649559 + 0.733201i
\(688\) 0.452294 0.111481i 0.0172436 0.00425016i
\(689\) −1.20812 1.62116i −0.0460257 0.0617614i
\(690\) 19.1334 + 4.71595i 0.728394 + 0.179533i
\(691\) −36.6835 + 25.3208i −1.39551 + 0.963249i −0.396530 + 0.918022i \(0.629786\pi\)
−0.998977 + 0.0452274i \(0.985599\pi\)
\(692\) 2.64527 + 0.652000i 0.100558 + 0.0247853i
\(693\) −65.3033 94.6081i −2.48067 3.59387i
\(694\) −12.8436 1.55949i −0.487535 0.0591975i
\(695\) 3.11297i 0.118082i
\(696\) −6.55802 + 0.796287i −0.248581 + 0.0301832i
\(697\) 42.6228 + 29.4204i 1.61445 + 1.11438i
\(698\) −0.976160 −0.0369482
\(699\) −64.3374 −2.43347
\(700\) 4.46876 + 3.08456i 0.168903 + 0.116585i
\(701\) 17.1493 9.00065i 0.647720 0.339950i −0.108663 0.994079i \(-0.534657\pi\)
0.756383 + 0.654129i \(0.226965\pi\)
\(702\) −10.2043 35.7634i −0.385135 1.34980i
\(703\) −1.18767 0.623336i −0.0447937 0.0235096i
\(704\) 9.90355 + 18.8696i 0.373254 + 0.711177i
\(705\) 9.32674 8.26277i 0.351265 0.311194i
\(706\) −4.41392 1.08793i −0.166120 0.0409449i
\(707\) −3.23690 + 6.16740i −0.121736 + 0.231949i
\(708\) 15.6015 + 29.7263i 0.586342 + 1.11718i
\(709\) 38.9393 + 14.7677i 1.46240 + 0.554613i 0.952208 0.305450i \(-0.0988068\pi\)
0.510187 + 0.860063i \(0.329576\pi\)
\(710\) 2.21014 8.96690i 0.0829452 0.336522i
\(711\) 32.7936 + 29.0526i 1.22986 + 1.08956i
\(712\) −8.49917 12.3132i −0.318520 0.461456i
\(713\) −17.1799 + 32.7336i −0.643394 + 1.22588i
\(714\) 55.1331 48.8437i 2.06331 1.82793i
\(715\) 11.9819 + 5.74426i 0.448098 + 0.214823i
\(716\) −15.0380 13.3225i −0.561996 0.497885i
\(717\) −37.5012 + 14.2223i −1.40051 + 0.531142i
\(718\) −3.27962 27.0101i −0.122394 1.00801i
\(719\) 3.90498 2.04949i 0.145631 0.0764331i −0.390334 0.920674i \(-0.627640\pi\)
0.535965 + 0.844240i \(0.319948\pi\)
\(720\) −1.64127 1.85261i −0.0611665 0.0690427i
\(721\) 37.2079 + 25.6828i 1.38569 + 0.956476i
\(722\) −1.32866 1.49975i −0.0494478 0.0558150i
\(723\) 14.4976 1.76033i 0.539172 0.0654673i
\(724\) −3.26197 26.8647i −0.121230 0.998419i
\(725\) −0.260248 + 0.686218i −0.00966537 + 0.0254855i
\(726\) −6.89652 2.61550i −0.255954 0.0970704i
\(727\) 28.7766 41.6900i 1.06726 1.54620i 0.251461 0.967867i \(-0.419089\pi\)
0.815802 0.578331i \(-0.196296\pi\)
\(728\) 15.8308 46.7956i 0.586728 1.73436i
\(729\) −3.30479 4.78782i −0.122400 0.177327i
\(730\) 2.46324 + 9.99376i 0.0911687 + 0.369886i
\(731\) 6.01908 + 3.15906i 0.222624 + 0.116842i
\(732\) 12.8087 33.7738i 0.473424 1.24832i
\(733\) −7.53910 + 2.85920i −0.278463 + 0.105607i −0.489883 0.871788i \(-0.662960\pi\)
0.211420 + 0.977395i \(0.432191\pi\)
\(734\) 10.3774 + 1.26004i 0.383036 + 0.0465090i
\(735\) 11.3263 + 45.9524i 0.417775 + 1.69498i
\(736\) 17.5088 + 33.3602i 0.645383 + 1.22967i
\(737\) 7.74172 11.2158i 0.285170 0.413140i
\(738\) 56.0678 13.8195i 2.06388 0.508702i
\(739\) 1.28416 5.21005i 0.0472386 0.191655i −0.942582 0.333975i \(-0.891610\pi\)
0.989821 + 0.142320i \(0.0454562\pi\)
\(740\) −0.133430 + 0.351826i −0.00490498 + 0.0129334i
\(741\) 42.2518 17.8027i 1.55216 0.653998i
\(742\) −0.864703 2.28003i −0.0317442 0.0837027i
\(743\) −25.6203 + 3.11086i −0.939917 + 0.114127i −0.576132 0.817357i \(-0.695439\pi\)
−0.363785 + 0.931483i \(0.618516\pi\)
\(744\) 42.7172 22.4197i 1.56609 0.821946i
\(745\) −6.95220 18.3315i −0.254709 0.671613i
\(746\) 19.7283i 0.722305i
\(747\) 109.259 41.4365i 3.99758 1.51608i
\(748\) −5.54506 + 22.4972i −0.202748 + 0.822579i
\(749\) 2.84066 3.20644i 0.103796 0.117161i
\(750\) −2.77391 + 0.683706i −0.101289 + 0.0249654i
\(751\) 35.9332 + 31.8341i 1.31122 + 1.16164i 0.975578 + 0.219653i \(0.0704927\pi\)
0.335645 + 0.941989i \(0.391046\pi\)
\(752\) −1.49395 0.181398i −0.0544786 0.00661490i
\(753\) 1.97935 16.3014i 0.0721315 0.594057i
\(754\) 2.42989 + 0.205937i 0.0884913 + 0.00749979i
\(755\) −0.332029 2.73451i −0.0120838 0.0995189i
\(756\) 60.7760i 2.21040i
\(757\) 2.20972 18.1987i 0.0803138 0.661443i −0.895842 0.444372i \(-0.853427\pi\)
0.976156 0.217071i \(-0.0696502\pi\)
\(758\) 11.5219 + 6.04714i 0.418493 + 0.219642i
\(759\) −73.6832 27.9444i −2.67453 1.01432i
\(760\) 7.89801 8.91501i 0.286491 0.323381i
\(761\) −16.6712 + 18.8179i −0.604329 + 0.682147i −0.968451 0.249205i \(-0.919831\pi\)
0.364121 + 0.931351i \(0.381369\pi\)
\(762\) 9.72411 + 3.68787i 0.352267 + 0.133597i
\(763\) −29.1764 15.3129i −1.05626 0.554366i
\(764\) 1.15370 9.50157i 0.0417394 0.343755i
\(765\) 36.1178i 1.30584i
\(766\) −4.22939 34.8322i −0.152814 1.25854i
\(767\) −9.31004 32.6293i −0.336166 1.17818i
\(768\) 6.24837 51.4600i 0.225469 1.85690i
\(769\) −1.22736 0.149029i −0.0442599 0.00537413i 0.0983768 0.995149i \(-0.468635\pi\)
−0.142637 + 0.989775i \(0.545558\pi\)
\(770\) 11.9958 + 10.6273i 0.432298 + 0.382983i
\(771\) 9.28318 2.28810i 0.334326 0.0824038i
\(772\) −2.67571 + 3.02025i −0.0963008 + 0.108701i
\(773\) −0.767330 + 3.11318i −0.0275989 + 0.111973i −0.983126 0.182931i \(-0.941442\pi\)
0.955527 + 0.294904i \(0.0952877\pi\)
\(774\) 7.08683 2.68768i 0.254731 0.0966067i
\(775\) 5.35954i 0.192520i
\(776\) 13.7115 + 36.1542i 0.492213 + 1.29786i
\(777\) −4.23552 + 2.22297i −0.151948 + 0.0797486i
\(778\) −1.81365 + 0.220218i −0.0650227 + 0.00789518i
\(779\) 13.7878 + 36.3554i 0.493999 + 1.30257i
\(780\) −6.38650 11.1645i −0.228673 0.399754i
\(781\) −13.0962 + 34.5319i −0.468619 + 1.23565i
\(782\) 8.31162 33.7216i 0.297223 1.20588i
\(783\) −7.97576 + 1.96585i −0.285031 + 0.0702537i
\(784\) 3.24709 4.70422i 0.115967 0.168008i
\(785\) 1.56617 + 2.98409i 0.0558991 + 0.106507i
\(786\) 0.762785 + 3.09474i 0.0272076 + 0.110386i
\(787\) 4.91376 + 0.596638i 0.175157 + 0.0212679i 0.207645 0.978204i \(-0.433420\pi\)
−0.0324884 + 0.999472i \(0.510343\pi\)
\(788\) −10.1827 + 3.86180i −0.362745 + 0.137571i
\(789\) 6.70538 17.6806i 0.238718 0.629447i
\(790\) −5.40819 2.83844i −0.192415 0.100987i
\(791\) −20.6743 83.8790i −0.735094 2.98239i
\(792\) 40.1831 + 58.2153i 1.42784 + 2.06859i
\(793\) −19.6356 + 30.7783i −0.697280 + 1.09297i
\(794\) 2.90771 4.21255i 0.103191 0.149498i
\(795\) −1.62540 0.616433i −0.0576470 0.0218626i
\(796\) 2.48524 6.55303i 0.0880869 0.232266i
\(797\) 1.18655 + 9.77210i 0.0420297 + 0.346145i 0.998520 + 0.0543820i \(0.0173189\pi\)
−0.956491 + 0.291763i \(0.905758\pi\)
\(798\) 54.8954 6.66550i 1.94327 0.235956i
\(799\) −14.5627 16.4379i −0.515192 0.581532i
\(800\) −4.49525 3.10285i −0.158931 0.109702i
\(801\) −22.5876 25.4961i −0.798093 0.900860i
\(802\) 21.8252 11.4547i 0.770674 0.404481i
\(803\) −4.96143 40.8610i −0.175085 1.44195i
\(804\) −12.3345 + 4.67787i −0.435005 + 0.164976i
\(805\) 24.3626 + 21.5834i 0.858671 + 0.760716i
\(806\) −17.1250 + 4.88622i −0.603202 + 0.172110i
\(807\) −65.3524 + 57.8972i −2.30051 + 2.03808i
\(808\) 1.99176 3.79499i 0.0700700 0.133507i
\(809\) −23.1016 33.4684i −0.812207 1.17669i −0.981565 0.191131i \(-0.938785\pi\)
0.169357 0.985555i \(-0.445831\pi\)
\(810\) −10.2552 9.08534i −0.360332 0.319226i
\(811\) −3.27087 + 13.2704i −0.114856 + 0.465988i 0.885144 + 0.465317i \(0.154060\pi\)
−1.00000 0.000670746i \(0.999786\pi\)
\(812\) −3.72613 1.41313i −0.130761 0.0495913i
\(813\) 44.4636 + 84.7182i 1.55941 + 2.97120i
\(814\) −0.516105 + 0.983356i −0.0180895 + 0.0344666i
\(815\) 16.4445 + 4.05322i 0.576027 + 0.141978i
\(816\) −4.74694 + 4.20542i −0.166176 + 0.147219i
\(817\) 2.37168 + 4.51886i 0.0829747 + 0.158095i
\(818\) −14.9659 7.85472i −0.523271 0.274634i
\(819\) 22.9368 110.105i 0.801475 3.84738i
\(820\) 9.65823 5.06903i 0.337280 0.177018i
\(821\) −4.23641 2.92418i −0.147852 0.102055i 0.491842 0.870684i \(-0.336324\pi\)
−0.639694 + 0.768630i \(0.720939\pi\)
\(822\) −52.5604 −1.83325
\(823\) 3.96142 0.138086 0.0690432 0.997614i \(-0.478005\pi\)
0.0690432 + 0.997614i \(0.478005\pi\)
\(824\) −22.8952 15.8034i −0.797591 0.550537i
\(825\) 11.3415 1.37711i 0.394862 0.0479449i
\(826\) 40.9247i 1.42395i
\(827\) 44.3669 + 5.38712i 1.54279 + 0.187328i 0.847263 0.531173i \(-0.178249\pi\)
0.695525 + 0.718502i \(0.255172\pi\)
\(828\) 29.8056 + 43.1809i 1.03582 + 1.50064i
\(829\) 9.44928 + 2.32904i 0.328187 + 0.0808908i 0.399967 0.916530i \(-0.369022\pi\)
−0.0717797 + 0.997421i \(0.522868\pi\)
\(830\) −13.4067 + 9.25401i −0.465355 + 0.321211i
\(831\) −58.0147 14.2993i −2.01251 0.496039i
\(832\) −6.68127 + 19.7497i −0.231631 + 0.684699i
\(833\) 80.9888 19.9620i 2.80610 0.691641i
\(834\) −5.89750 + 6.65690i −0.204214 + 0.230510i
\(835\) −2.72460 + 3.94726i −0.0942887 + 0.136601i
\(836\) −13.0206 + 11.5353i −0.450328 + 0.398956i
\(837\) 49.3691 34.0770i 1.70645 1.17787i
\(838\) 19.3623 13.3648i 0.668860 0.461681i
\(839\) −19.0397 + 36.2771i −0.657323 + 1.25242i 0.297351 + 0.954768i \(0.403897\pi\)
−0.954673 + 0.297655i \(0.903795\pi\)
\(840\) −10.1650 41.2409i −0.350725 1.42295i
\(841\) −3.43064 + 28.2539i −0.118298 + 0.974271i
\(842\) 2.40673 + 6.34602i 0.0829413 + 0.218698i
\(843\) −12.4440 14.0464i −0.428596 0.483785i
\(844\) −13.2675 −0.456685
\(845\) 4.01801 + 12.3635i 0.138224 + 0.425317i
\(846\) −24.4860 −0.841846
\(847\) −8.07854 9.11879i −0.277582 0.313325i
\(848\) 0.0744505 + 0.196310i 0.00255664 + 0.00674130i
\(849\) −6.25930 + 51.5499i −0.214818 + 1.76919i
\(850\) 1.20500 + 4.88887i 0.0413311 + 0.167687i
\(851\) −1.04817 + 1.99713i −0.0359310 + 0.0684607i
\(852\) 29.4209 20.3078i 1.00794 0.695732i
\(853\) 5.79611 4.00077i 0.198455 0.136984i −0.464693 0.885472i \(-0.653835\pi\)
0.663148 + 0.748488i \(0.269220\pi\)
\(854\) −32.9588 + 29.1989i −1.12783 + 0.999167i
\(855\) 15.4035 22.3158i 0.526787 0.763183i
\(856\) −1.74795 + 1.97302i −0.0597436 + 0.0674365i
\(857\) 15.5278 3.82727i 0.530421 0.130737i 0.0349955 0.999387i \(-0.488858\pi\)
0.495425 + 0.868650i \(0.335012\pi\)
\(858\) −14.7401 34.9833i −0.503219 1.19431i
\(859\) 49.6464 + 12.2367i 1.69391 + 0.417512i 0.963973 0.265999i \(-0.0857017\pi\)
0.729940 + 0.683511i \(0.239548\pi\)
\(860\) 1.17824 0.813281i 0.0401777 0.0277327i
\(861\) 134.634 + 33.1843i 4.58831 + 1.13092i
\(862\) 5.67633 + 8.22359i 0.193337 + 0.280097i
\(863\) −11.1891 1.35861i −0.380883 0.0462475i −0.0721434 0.997394i \(-0.522984\pi\)
−0.308739 + 0.951147i \(0.599907\pi\)
\(864\) 61.1363i 2.07990i
\(865\) −2.35034 + 0.285382i −0.0799138 + 0.00970329i
\(866\) −5.73429 3.95810i −0.194859 0.134502i
\(867\) −39.8432 −1.35315
\(868\) 29.1020 0.987788
\(869\) 20.1015 + 13.8750i 0.681896 + 0.470679i
\(870\) 1.85656 0.974396i 0.0629432 0.0330351i
\(871\) 13.1690 2.08619i 0.446213 0.0706878i
\(872\) 17.9531 + 9.42252i 0.607969 + 0.319087i
\(873\) 40.9101 + 77.9476i 1.38460 + 2.63813i
\(874\) 19.5169 17.2905i 0.660170 0.584860i
\(875\) −4.58163 1.12927i −0.154887 0.0381763i
\(876\) −18.5159 + 35.2791i −0.625595 + 1.19197i
\(877\) 3.86637 + 7.36675i 0.130558 + 0.248757i 0.941956 0.335737i \(-0.108985\pi\)
−0.811398 + 0.584494i \(0.801293\pi\)
\(878\) −27.7402 10.5205i −0.936185 0.355048i
\(879\) −10.5379 + 42.7541i −0.355436 + 1.44206i
\(880\) −1.03283 0.915009i −0.0348167 0.0308449i
\(881\) −9.39951 13.6175i −0.316677 0.458787i 0.632029 0.774945i \(-0.282222\pi\)
−0.948706 + 0.316158i \(0.897607\pi\)
\(882\) 43.2211 82.3509i 1.45533 2.77290i
\(883\) −41.6499 + 36.8986i −1.40163 + 1.24174i −0.467889 + 0.883787i \(0.654985\pi\)
−0.933741 + 0.357949i \(0.883476\pi\)
\(884\) −19.6769 + 11.2559i −0.661807 + 0.378576i
\(885\) −21.8375 19.3463i −0.734059 0.650319i
\(886\) 3.25909 1.23601i 0.109491 0.0415245i
\(887\) −3.68416 30.3418i −0.123702 1.01878i −0.913904 0.405931i \(-0.866947\pi\)
0.790201 0.612847i \(-0.209976\pi\)
\(888\) 2.60624 1.36786i 0.0874598 0.0459024i
\(889\) 11.3908 + 12.8575i 0.382034 + 0.431228i
\(890\) 3.90806 + 2.69754i 0.130998 + 0.0904216i
\(891\) 36.3323 + 41.0107i 1.21718 + 1.37391i
\(892\) −23.4505 + 2.84741i −0.785181 + 0.0953382i
\(893\) −1.98732 16.3670i −0.0665030 0.547701i
\(894\) −19.8619 + 52.3716i −0.664282 + 1.75157i
\(895\) 16.3246 + 6.19110i 0.545671 + 0.206946i
\(896\) 14.9985 21.7290i 0.501063 0.725915i
\(897\) −29.9362 71.0488i −0.999541 2.37225i
\(898\) 3.40721 + 4.93620i 0.113700 + 0.164723i
\(899\) 0.941329 + 3.81912i 0.0313951 + 0.127375i
\(900\) −6.73547 3.53505i −0.224516 0.117835i
\(901\) −1.08643 + 2.86469i −0.0361943 + 0.0954366i
\(902\) 30.1013 11.4159i 1.00226 0.380108i
\(903\) 18.0674 + 2.19378i 0.601245 + 0.0730044i
\(904\) 12.7215 + 51.6133i 0.423112 + 1.71663i
\(905\) 10.9291 + 20.8237i 0.363297 + 0.692204i
\(906\) −4.47047 + 6.47660i −0.148521 + 0.215171i
\(907\) −19.7809 + 4.87555i −0.656813 + 0.161890i −0.553617 0.832771i \(-0.686753\pi\)
−0.103196 + 0.994661i \(0.532907\pi\)
\(908\) −1.95878 + 7.94708i −0.0650044 + 0.263733i
\(909\) 3.46007 9.12346i 0.114763 0.302606i
\(910\) 0.568732 + 15.6689i 0.0188533 + 0.519420i
\(911\) −0.178853 0.471596i −0.00592565 0.0156247i 0.932021 0.362405i \(-0.118044\pi\)
−0.937946 + 0.346780i \(0.887275\pi\)
\(912\) −4.72646 + 0.573896i −0.156509 + 0.0190036i
\(913\) 57.6834 30.2746i 1.90904 1.00194i
\(914\) 9.59358 + 25.2962i 0.317328 + 0.836724i
\(915\) 31.3901i 1.03772i
\(916\) 8.91084 3.37944i 0.294422 0.111660i
\(917\) −1.25988 + 5.11155i −0.0416050 + 0.168798i
\(918\) −37.3719 + 42.1842i −1.23346 + 1.39229i
\(919\) 55.4037 13.6558i 1.82760 0.450463i 0.832912 0.553406i \(-0.186672\pi\)
0.994687 + 0.102944i \(0.0328261\pi\)
\(920\) −14.9911 13.2809i −0.494241 0.437860i
\(921\) 94.7741 + 11.5077i 3.12291 + 0.379190i
\(922\) −3.85888 + 31.7807i −0.127085 + 1.04664i
\(923\) −33.2972 + 14.0297i −1.09599 + 0.461793i
\(924\) 7.47765 + 61.5840i 0.245997 + 2.02596i
\(925\) 0.326994i 0.0107515i
\(926\) −4.07836 + 33.5883i −0.134023 + 1.10378i
\(927\) −56.0811 29.4336i −1.84194 0.966727i
\(928\) 3.74821 + 1.42151i 0.123041 + 0.0466634i
\(929\) −28.3131 + 31.9589i −0.928923 + 1.04854i 0.0697772 + 0.997563i \(0.477771\pi\)
−0.998700 + 0.0509745i \(0.983767\pi\)
\(930\) −10.1536 + 11.4610i −0.332950 + 0.375823i
\(931\) 58.5531 + 22.2063i 1.91900 + 0.727781i
\(932\) 21.1459 + 11.0982i 0.692658 + 0.363535i
\(933\) 3.09181 25.4633i 0.101221 0.833631i
\(934\) 12.7878i 0.418430i
\(935\) −2.42709 19.9889i −0.0793744 0.653707i
\(936\) −14.1137 + 67.7509i −0.461320 + 2.21451i
\(937\) −6.42717 + 52.9325i −0.209966 + 1.72923i 0.382780 + 0.923839i \(0.374967\pi\)
−0.592747 + 0.805389i \(0.701956\pi\)
\(938\) 15.9638 + 1.93836i 0.521238 + 0.0632897i
\(939\) −1.87547 1.66152i −0.0612037 0.0542218i
\(940\) −4.49077 + 1.10688i −0.146473 + 0.0361023i
\(941\) 14.6929 16.5849i 0.478976 0.540652i −0.458503 0.888693i \(-0.651614\pi\)
0.937480 + 0.348040i \(0.113153\pi\)
\(942\) 2.30417 9.34839i 0.0750740 0.304587i
\(943\) 61.1337 23.1849i 1.99079 0.755005i
\(944\) 3.52359i 0.114683i
\(945\) −18.7287 49.3836i −0.609245 1.60645i
\(946\) 3.74149 1.96369i 0.121646 0.0638450i
\(947\) −20.9037 + 2.53817i −0.679278 + 0.0824793i −0.452902 0.891560i \(-0.649611\pi\)
−0.226377 + 0.974040i \(0.572688\pi\)
\(948\) −8.38387 22.1065i −0.272295 0.717984i
\(949\) 25.5930 31.0913i 0.830784 1.00927i
\(950\) −1.34048 + 3.53454i −0.0434908 + 0.114676i
\(951\) −5.49567 + 22.2968i −0.178209 + 0.723024i
\(952\) −72.6850 + 17.9153i −2.35574 + 0.580637i
\(953\) 17.0985 24.7715i 0.553876 0.802427i −0.441623 0.897201i \(-0.645597\pi\)
0.995499 + 0.0947732i \(0.0302126\pi\)
\(954\) 1.58753 + 3.02478i 0.0513982 + 0.0979310i
\(955\) 1.99056 + 8.07604i 0.0644131 + 0.261334i
\(956\) 14.7790 + 1.79449i 0.477986 + 0.0580380i
\(957\) −7.83992 + 2.97329i −0.253429 + 0.0961129i
\(958\) 4.28382 11.2955i 0.138404 0.364941i
\(959\) −76.8695 40.3442i −2.48225 1.30278i
\(960\) 4.29005 + 17.4054i 0.138461 + 0.561758i
\(961\) 1.29252 + 1.87254i 0.0416942 + 0.0604044i
\(962\) −1.04482 + 0.298116i −0.0336864 + 0.00961165i
\(963\) −3.40901 + 4.93881i −0.109854 + 0.159151i
\(964\) −5.06862 1.92227i −0.163249 0.0619123i
\(965\) 1.24343 3.27865i 0.0400274 0.105543i
\(966\) −11.2084 92.3096i −0.360625 2.97001i
\(967\) −33.5237 + 4.07052i −1.07805 + 0.130899i −0.640245 0.768171i \(-0.721167\pi\)
−0.437805 + 0.899070i \(0.644244\pi\)
\(968\) 4.97097 + 5.61107i 0.159773 + 0.180347i
\(969\) −57.1796 39.4682i −1.83687 1.26790i
\(970\) −8.13811 9.18603i −0.261299 0.294945i
\(971\) −17.3029 + 9.08126i −0.555276 + 0.291432i −0.718926 0.695087i \(-0.755366\pi\)
0.163649 + 0.986519i \(0.447673\pi\)
\(972\) −1.73524 14.2909i −0.0556577 0.458382i
\(973\) −13.7348 + 5.20891i −0.440317 + 0.166990i
\(974\) −1.00285 0.888447i −0.0321334 0.0284677i
\(975\) 8.62982 + 7.10369i 0.276375 + 0.227500i
\(976\) 2.83774 2.51401i 0.0908337 0.0804716i
\(977\) −7.80196 + 14.8654i −0.249607 + 0.475586i −0.977732 0.209858i \(-0.932700\pi\)
0.728125 + 0.685445i \(0.240392\pi\)
\(978\) −27.4869 39.8216i −0.878933 1.27335i
\(979\) −14.2141 12.5926i −0.454284 0.402461i
\(980\) 4.20419 17.0571i 0.134298 0.544868i
\(981\) 43.1607 + 16.3687i 1.37802 + 0.522613i
\(982\) −4.60147 8.76736i −0.146839 0.279778i
\(983\) 14.0007 26.6761i 0.446553 0.850835i −0.553288 0.832990i \(-0.686627\pi\)
0.999841 0.0178450i \(-0.00568055\pi\)
\(984\) −82.8444 20.4193i −2.64098 0.650944i
\(985\) 7.08394 6.27582i 0.225713 0.199964i
\(986\) −1.71732 3.27209i −0.0546908 0.104205i
\(987\) −52.0626 27.3246i −1.65717 0.869750i
\(988\) −16.9580 1.43722i −0.539505 0.0457240i
\(989\) 7.59872 3.98812i 0.241625 0.126815i
\(990\) −18.4768 12.7536i −0.587232 0.405337i
\(991\) −27.9816 −0.888866 −0.444433 0.895812i \(-0.646595\pi\)
−0.444433 + 0.895812i \(0.646595\pi\)
\(992\) −29.2745 −0.929468
\(993\) 52.7817 + 36.4326i 1.67498 + 1.15615i
\(994\) −43.2612 + 5.25286i −1.37216 + 0.166611i
\(995\) 6.09052i 0.193083i
\(996\) −62.5992 7.60092i −1.98353 0.240844i
\(997\) 6.52069 + 9.44685i 0.206512 + 0.299185i 0.912530 0.409009i \(-0.134126\pi\)
−0.706018 + 0.708194i \(0.749510\pi\)
\(998\) 12.1452 + 2.99352i 0.384449 + 0.0947582i
\(999\) 3.01209 2.07909i 0.0952982 0.0657796i
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 845.2.w.a.116.23 yes 744
169.51 even 26 inner 845.2.w.a.51.23 744
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.w.a.51.23 744 169.51 even 26 inner
845.2.w.a.116.23 yes 744 1.1 even 1 trivial