Properties

Label 950.2.r.b.11.19
Level $950$
Weight $2$
Character 950.11
Analytic conductor $7.586$
Analytic rank $0$
Dimension $200$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(11,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([24, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.r (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(25\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 11.19
Character \(\chi\) \(=\) 950.11
Dual form 950.2.r.b.691.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.104528 - 0.994522i) q^{2} +(0.942721 + 1.04700i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.192905 - 2.22773i) q^{5} +(0.942721 - 1.04700i) q^{6} -0.469500 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.106104 - 1.00951i) q^{9} +O(q^{10})\) \(q+(-0.104528 - 0.994522i) q^{2} +(0.942721 + 1.04700i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.192905 - 2.22773i) q^{5} +(0.942721 - 1.04700i) q^{6} -0.469500 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.106104 - 1.00951i) q^{9} +(-2.19536 + 0.424709i) q^{10} +(-2.43821 + 1.77146i) q^{11} +(-1.13980 - 0.828116i) q^{12} +(0.275955 - 2.62554i) q^{13} +(0.0490761 + 0.466928i) q^{14} +(2.15057 - 2.30210i) q^{15} +(0.913545 - 0.406737i) q^{16} +(1.06644 + 0.226679i) q^{17} -1.01507 q^{18} +(1.40110 - 4.12758i) q^{19} +(0.651861 + 2.13894i) q^{20} +(-0.442608 - 0.491566i) q^{21} +(2.01662 + 2.23969i) q^{22} +(-6.69911 - 2.98264i) q^{23} +(-0.704437 + 1.22012i) q^{24} +(-4.92558 + 0.859480i) q^{25} -2.64000 q^{26} +(4.57639 - 3.32494i) q^{27} +(0.459241 - 0.0976146i) q^{28} +(-2.80886 + 0.597042i) q^{29} +(-2.51429 - 1.89816i) q^{30} +(-1.23295 - 3.79462i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.15327 - 0.882805i) q^{33} +(0.113964 - 1.08429i) q^{34} +(0.0905688 + 1.04592i) q^{35} +(0.106104 + 1.00951i) q^{36} +(0.287378 + 0.208792i) q^{37} +(-4.25142 - 0.961971i) q^{38} +(3.00908 - 2.18623i) q^{39} +(2.05909 - 0.871870i) q^{40} +(3.43154 - 1.52782i) q^{41} +(-0.442608 + 0.491566i) q^{42} +(-0.328737 + 0.569390i) q^{43} +(2.01662 - 2.23969i) q^{44} +(-2.26939 - 0.0416316i) q^{45} +(-2.26605 + 6.97418i) q^{46} +(9.01672 - 1.91656i) q^{47} +(1.28707 + 0.573041i) q^{48} -6.77957 q^{49} +(1.36963 + 4.80875i) q^{50} +(0.768024 + 1.33026i) q^{51} +(0.275955 + 2.62554i) q^{52} +(-7.54192 + 1.60308i) q^{53} +(-3.78509 - 4.20377i) q^{54} +(4.41669 + 5.08996i) q^{55} +(-0.145084 - 0.446521i) q^{56} +(5.64241 - 2.42421i) q^{57} +(0.887377 + 2.73107i) q^{58} +(6.83891 - 3.04488i) q^{59} +(-1.62495 + 2.69892i) q^{60} +(-7.72127 - 3.43773i) q^{61} +(-3.64496 + 1.62284i) q^{62} +(-0.0498159 + 0.473966i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-5.90223 - 0.108275i) q^{65} +(-0.443834 + 4.22280i) q^{66} +(3.10707 - 3.45075i) q^{67} -1.09027 q^{68} +(-3.19258 - 9.82575i) q^{69} +(1.03072 - 0.199401i) q^{70} +(5.41543 + 6.01444i) q^{71} +(0.992891 - 0.211046i) q^{72} +(-1.22144 - 11.6212i) q^{73} +(0.177609 - 0.307628i) q^{74} +(-5.54332 - 4.34682i) q^{75} +(-0.512306 + 4.32869i) q^{76} +(1.14474 - 0.831703i) q^{77} +(-2.48879 - 2.76408i) q^{78} +(-3.52171 - 3.91125i) q^{79} +(-1.08233 - 1.95667i) q^{80} +(4.81680 + 1.02384i) q^{81} +(-1.87814 - 3.25304i) q^{82} +(0.866993 + 2.66833i) q^{83} +(0.535138 + 0.388800i) q^{84} +(0.299258 - 2.41947i) q^{85} +(0.600633 + 0.267419i) q^{86} +(-3.27307 - 2.37803i) q^{87} +(-2.43821 - 1.77146i) q^{88} +(6.04628 + 2.69198i) q^{89} +(0.195812 + 2.26131i) q^{90} +(-0.129561 + 1.23269i) q^{91} +(7.17284 + 1.52464i) q^{92} +(2.81064 - 4.86816i) q^{93} +(-2.84857 - 8.76699i) q^{94} +(-9.46542 - 2.32504i) q^{95} +(0.435366 - 1.33992i) q^{96} +(-5.03176 - 5.58834i) q^{97} +(0.708658 + 6.74243i) q^{98} +(1.52961 + 2.64936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.104528 0.994522i −0.0739128 0.703233i
\(3\) 0.942721 + 1.04700i 0.544280 + 0.604484i 0.951046 0.309048i \(-0.100010\pi\)
−0.406766 + 0.913532i \(0.633344\pi\)
\(4\) −0.978148 + 0.207912i −0.489074 + 0.103956i
\(5\) −0.192905 2.22773i −0.0862696 0.996272i
\(6\) 0.942721 1.04700i 0.384864 0.427435i
\(7\) −0.469500 −0.177454 −0.0887272 0.996056i \(-0.528280\pi\)
−0.0887272 + 0.996056i \(0.528280\pi\)
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) 0.106104 1.00951i 0.0353680 0.336504i
\(10\) −2.19536 + 0.424709i −0.694235 + 0.134305i
\(11\) −2.43821 + 1.77146i −0.735148 + 0.534117i −0.891188 0.453634i \(-0.850127\pi\)
0.156039 + 0.987751i \(0.450127\pi\)
\(12\) −1.13980 0.828116i −0.329033 0.239056i
\(13\) 0.275955 2.62554i 0.0765363 0.728194i −0.887209 0.461368i \(-0.847359\pi\)
0.963745 0.266825i \(-0.0859747\pi\)
\(14\) 0.0490761 + 0.466928i 0.0131161 + 0.124792i
\(15\) 2.15057 2.30210i 0.555276 0.594400i
\(16\) 0.913545 0.406737i 0.228386 0.101684i
\(17\) 1.06644 + 0.226679i 0.258650 + 0.0549777i 0.335411 0.942072i \(-0.391125\pi\)
−0.0767616 + 0.997049i \(0.524458\pi\)
\(18\) −1.01507 −0.239255
\(19\) 1.40110 4.12758i 0.321433 0.946932i
\(20\) 0.651861 + 2.13894i 0.145760 + 0.478282i
\(21\) −0.442608 0.491566i −0.0965849 0.107268i
\(22\) 2.01662 + 2.23969i 0.429945 + 0.477503i
\(23\) −6.69911 2.98264i −1.39686 0.621923i −0.436252 0.899825i \(-0.643694\pi\)
−0.960609 + 0.277902i \(0.910361\pi\)
\(24\) −0.704437 + 1.22012i −0.143793 + 0.249056i
\(25\) −4.92558 + 0.859480i −0.985115 + 0.171896i
\(26\) −2.64000 −0.517747
\(27\) 4.57639 3.32494i 0.880727 0.639886i
\(28\) 0.459241 0.0976146i 0.0867883 0.0184474i
\(29\) −2.80886 + 0.597042i −0.521592 + 0.110868i −0.461182 0.887306i \(-0.652574\pi\)
−0.0604106 + 0.998174i \(0.519241\pi\)
\(30\) −2.51429 1.89816i −0.459044 0.346555i
\(31\) −1.23295 3.79462i −0.221444 0.681534i −0.998633 0.0522674i \(-0.983355\pi\)
0.777189 0.629267i \(-0.216645\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −4.15327 0.882805i −0.722992 0.153677i
\(34\) 0.113964 1.08429i 0.0195446 0.185955i
\(35\) 0.0905688 + 1.04592i 0.0153089 + 0.176793i
\(36\) 0.106104 + 1.00951i 0.0176840 + 0.168252i
\(37\) 0.287378 + 0.208792i 0.0472446 + 0.0343252i 0.611157 0.791509i \(-0.290704\pi\)
−0.563912 + 0.825835i \(0.690704\pi\)
\(38\) −4.25142 0.961971i −0.689672 0.156052i
\(39\) 3.00908 2.18623i 0.481839 0.350077i
\(40\) 2.05909 0.871870i 0.325570 0.137855i
\(41\) 3.43154 1.52782i 0.535916 0.238605i −0.120888 0.992666i \(-0.538574\pi\)
0.656805 + 0.754061i \(0.271908\pi\)
\(42\) −0.442608 + 0.491566i −0.0682959 + 0.0758502i
\(43\) −0.328737 + 0.569390i −0.0501320 + 0.0868312i −0.890002 0.455956i \(-0.849298\pi\)
0.839870 + 0.542787i \(0.182631\pi\)
\(44\) 2.01662 2.23969i 0.304017 0.337645i
\(45\) −2.26939 0.0416316i −0.338301 0.00620607i
\(46\) −2.26605 + 6.97418i −0.334111 + 1.02829i
\(47\) 9.01672 1.91656i 1.31522 0.279559i 0.503700 0.863879i \(-0.331972\pi\)
0.811524 + 0.584320i \(0.198639\pi\)
\(48\) 1.28707 + 0.573041i 0.185773 + 0.0827113i
\(49\) −6.77957 −0.968510
\(50\) 1.36963 + 4.80875i 0.193696 + 0.680060i
\(51\) 0.768024 + 1.33026i 0.107545 + 0.186273i
\(52\) 0.275955 + 2.62554i 0.0382681 + 0.364097i
\(53\) −7.54192 + 1.60308i −1.03596 + 0.220201i −0.694348 0.719640i \(-0.744307\pi\)
−0.341615 + 0.939840i \(0.610974\pi\)
\(54\) −3.78509 4.20377i −0.515086 0.572061i
\(55\) 4.41669 + 5.08996i 0.595546 + 0.686330i
\(56\) −0.145084 0.446521i −0.0193876 0.0596689i
\(57\) 5.64241 2.42421i 0.747356 0.321095i
\(58\) 0.887377 + 2.73107i 0.116518 + 0.358606i
\(59\) 6.83891 3.04488i 0.890350 0.396409i 0.0899994 0.995942i \(-0.471313\pi\)
0.800350 + 0.599533i \(0.204647\pi\)
\(60\) −1.62495 + 2.69892i −0.209780 + 0.348429i
\(61\) −7.72127 3.43773i −0.988607 0.440156i −0.152250 0.988342i \(-0.548652\pi\)
−0.836357 + 0.548186i \(0.815319\pi\)
\(62\) −3.64496 + 1.62284i −0.462910 + 0.206101i
\(63\) −0.0498159 + 0.473966i −0.00627621 + 0.0597141i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −5.90223 0.108275i −0.732082 0.0134299i
\(66\) −0.443834 + 4.22280i −0.0546322 + 0.519791i
\(67\) 3.10707 3.45075i 0.379589 0.421577i −0.522829 0.852438i \(-0.675123\pi\)
0.902418 + 0.430861i \(0.141790\pi\)
\(68\) −1.09027 −0.132214
\(69\) −3.19258 9.82575i −0.384341 1.18288i
\(70\) 1.03072 0.199401i 0.123195 0.0238330i
\(71\) 5.41543 + 6.01444i 0.642693 + 0.713783i 0.973184 0.230026i \(-0.0738811\pi\)
−0.330491 + 0.943809i \(0.607214\pi\)
\(72\) 0.992891 0.211046i 0.117013 0.0248720i
\(73\) −1.22144 11.6212i −0.142958 1.36016i −0.797128 0.603810i \(-0.793648\pi\)
0.654170 0.756348i \(-0.273018\pi\)
\(74\) 0.177609 0.307628i 0.0206467 0.0357611i
\(75\) −5.54332 4.34682i −0.640087 0.501927i
\(76\) −0.512306 + 4.32869i −0.0587656 + 0.496535i
\(77\) 1.14474 0.831703i 0.130455 0.0947814i
\(78\) −2.48879 2.76408i −0.281800 0.312970i
\(79\) −3.52171 3.91125i −0.396223 0.440050i 0.511715 0.859155i \(-0.329010\pi\)
−0.907938 + 0.419105i \(0.862344\pi\)
\(80\) −1.08233 1.95667i −0.121008 0.218763i
\(81\) 4.81680 + 1.02384i 0.535200 + 0.113760i
\(82\) −1.87814 3.25304i −0.207406 0.359238i
\(83\) 0.866993 + 2.66833i 0.0951648 + 0.292887i 0.987297 0.158888i \(-0.0507909\pi\)
−0.892132 + 0.451775i \(0.850791\pi\)
\(84\) 0.535138 + 0.388800i 0.0583883 + 0.0424216i
\(85\) 0.299258 2.41947i 0.0324591 0.262428i
\(86\) 0.600633 + 0.267419i 0.0647679 + 0.0288365i
\(87\) −3.27307 2.37803i −0.350910 0.254951i
\(88\) −2.43821 1.77146i −0.259914 0.188839i
\(89\) 6.04628 + 2.69198i 0.640904 + 0.285349i 0.701344 0.712823i \(-0.252584\pi\)
−0.0604399 + 0.998172i \(0.519250\pi\)
\(90\) 0.195812 + 2.26131i 0.0206404 + 0.238363i
\(91\) −0.129561 + 1.23269i −0.0135817 + 0.129221i
\(92\) 7.17284 + 1.52464i 0.747821 + 0.158954i
\(93\) 2.81064 4.86816i 0.291449 0.504805i
\(94\) −2.84857 8.76699i −0.293807 0.904246i
\(95\) −9.46542 2.32504i −0.971132 0.238544i
\(96\) 0.435366 1.33992i 0.0444344 0.136755i
\(97\) −5.03176 5.58834i −0.510898 0.567410i 0.431410 0.902156i \(-0.358016\pi\)
−0.942308 + 0.334746i \(0.891349\pi\)
\(98\) 0.708658 + 6.74243i 0.0715853 + 0.681088i
\(99\) 1.52961 + 2.64936i 0.153732 + 0.266271i
\(100\) 4.63924 1.86478i 0.463924 0.186478i
\(101\) 1.09596 + 1.89827i 0.109053 + 0.188885i 0.915387 0.402576i \(-0.131885\pi\)
−0.806334 + 0.591460i \(0.798552\pi\)
\(102\) 1.24269 0.902866i 0.123044 0.0893970i
\(103\) 1.78929 5.50686i 0.176304 0.542607i −0.823387 0.567480i \(-0.807918\pi\)
0.999691 + 0.0248735i \(0.00791830\pi\)
\(104\) 2.58231 0.548887i 0.253217 0.0538228i
\(105\) −1.00970 + 1.08084i −0.0985362 + 0.105479i
\(106\) 2.38265 + 7.33304i 0.231423 + 0.712248i
\(107\) 15.3436 1.48332 0.741661 0.670775i \(-0.234038\pi\)
0.741661 + 0.670775i \(0.234038\pi\)
\(108\) −3.78509 + 4.20377i −0.364221 + 0.404508i
\(109\) −9.60191 + 4.27505i −0.919696 + 0.409475i −0.811298 0.584633i \(-0.801239\pi\)
−0.108398 + 0.994108i \(0.534572\pi\)
\(110\) 4.60040 4.92454i 0.438631 0.469536i
\(111\) 0.0523122 + 0.497717i 0.00496525 + 0.0472412i
\(112\) −0.428910 + 0.190963i −0.0405282 + 0.0180443i
\(113\) 8.82422 + 6.41117i 0.830113 + 0.603112i 0.919591 0.392876i \(-0.128520\pi\)
−0.0894782 + 0.995989i \(0.528520\pi\)
\(114\) −3.00073 5.35810i −0.281044 0.501832i
\(115\) −5.35222 + 15.4992i −0.499097 + 1.44531i
\(116\) 2.62335 1.16799i 0.243572 0.108445i
\(117\) −2.62124 0.557161i −0.242333 0.0515095i
\(118\) −3.74306 6.48317i −0.344576 0.596824i
\(119\) −0.500694 0.106426i −0.0458986 0.00975604i
\(120\) 2.85399 + 1.33393i 0.260533 + 0.121771i
\(121\) −0.592397 + 1.82321i −0.0538543 + 0.165746i
\(122\) −2.61181 + 8.03831i −0.236462 + 0.727754i
\(123\) 4.83461 + 2.15251i 0.435922 + 0.194085i
\(124\) 1.99495 + 3.45536i 0.179152 + 0.310300i
\(125\) 2.86486 + 10.8071i 0.256241 + 0.966613i
\(126\) 0.476577 0.0424568
\(127\) −3.89669 1.73492i −0.345775 0.153949i 0.226499 0.974011i \(-0.427272\pi\)
−0.572274 + 0.820062i \(0.693939\pi\)
\(128\) 0.669131 + 0.743145i 0.0591433 + 0.0656853i
\(129\) −0.906058 + 0.192589i −0.0797739 + 0.0169565i
\(130\) 0.509269 + 5.88122i 0.0446658 + 0.515817i
\(131\) 10.0938 + 2.14551i 0.881903 + 0.187454i 0.626538 0.779391i \(-0.284471\pi\)
0.255365 + 0.966845i \(0.417805\pi\)
\(132\) 4.24606 0.369572
\(133\) −0.657815 + 1.93790i −0.0570398 + 0.168037i
\(134\) −3.75663 2.72935i −0.324523 0.235780i
\(135\) −8.28989 9.55358i −0.713480 0.822241i
\(136\) 0.113964 + 1.08429i 0.00977231 + 0.0929774i
\(137\) −1.75734 + 16.7200i −0.150140 + 1.42848i 0.616979 + 0.786980i \(0.288356\pi\)
−0.767119 + 0.641505i \(0.778310\pi\)
\(138\) −9.43821 + 4.20216i −0.803433 + 0.357712i
\(139\) 14.4227 + 6.42139i 1.22331 + 0.544655i 0.913771 0.406230i \(-0.133157\pi\)
0.309544 + 0.950885i \(0.399824\pi\)
\(140\) −0.306049 1.00423i −0.0258658 0.0848733i
\(141\) 10.5069 + 7.63370i 0.884839 + 0.642873i
\(142\) 5.41543 6.01444i 0.454453 0.504721i
\(143\) 3.97821 + 6.89047i 0.332675 + 0.576210i
\(144\) −0.313675 0.965392i −0.0261396 0.0804493i
\(145\) 1.87189 + 6.14221i 0.155452 + 0.510083i
\(146\) −11.4299 + 2.42949i −0.945942 + 0.201066i
\(147\) −6.39124 7.09819i −0.527141 0.585449i
\(148\) −0.324508 0.144480i −0.0266744 0.0118762i
\(149\) −8.32086 + 14.4122i −0.681672 + 1.18069i 0.292799 + 0.956174i \(0.405413\pi\)
−0.974470 + 0.224516i \(0.927920\pi\)
\(150\) −3.74357 + 5.96732i −0.305661 + 0.487229i
\(151\) 4.14501 0.337316 0.168658 0.985675i \(-0.446057\pi\)
0.168658 + 0.985675i \(0.446057\pi\)
\(152\) 4.35853 + 0.0570286i 0.353523 + 0.00462563i
\(153\) 0.341989 1.05253i 0.0276482 0.0850923i
\(154\) −0.946805 1.05153i −0.0762957 0.0847350i
\(155\) −8.21556 + 3.47868i −0.659890 + 0.279414i
\(156\) −2.48879 + 2.76408i −0.199262 + 0.221303i
\(157\) 9.15353 15.8544i 0.730532 1.26532i −0.226125 0.974098i \(-0.572606\pi\)
0.956656 0.291219i \(-0.0940610\pi\)
\(158\) −3.52171 + 3.91125i −0.280172 + 0.311162i
\(159\) −8.78835 6.38511i −0.696962 0.506372i
\(160\) −1.83282 + 1.28093i −0.144897 + 0.101266i
\(161\) 3.14523 + 1.40035i 0.247879 + 0.110363i
\(162\) 0.514741 4.89743i 0.0404419 0.384779i
\(163\) −2.53103 1.83890i −0.198245 0.144034i 0.484234 0.874938i \(-0.339098\pi\)
−0.682479 + 0.730905i \(0.739098\pi\)
\(164\) −3.03890 + 2.20789i −0.237298 + 0.172407i
\(165\) −1.16547 + 9.42267i −0.0907315 + 0.733554i
\(166\) 2.56309 1.14116i 0.198934 0.0885712i
\(167\) −1.78279 + 1.97999i −0.137957 + 0.153217i −0.808164 0.588957i \(-0.799539\pi\)
0.670207 + 0.742174i \(0.266205\pi\)
\(168\) 0.330733 0.572847i 0.0255166 0.0441961i
\(169\) 5.89861 + 1.25379i 0.453739 + 0.0964452i
\(170\) −2.43750 0.0447155i −0.186948 0.00342952i
\(171\) −4.01818 1.85238i −0.307278 0.141655i
\(172\) 0.203171 0.625296i 0.0154916 0.0476784i
\(173\) −2.26220 21.5234i −0.171992 1.63640i −0.651350 0.758777i \(-0.725797\pi\)
0.479358 0.877619i \(-0.340869\pi\)
\(174\) −2.02287 + 3.50371i −0.153353 + 0.265616i
\(175\) 2.31256 0.403526i 0.174813 0.0305037i
\(176\) −1.50690 + 2.61002i −0.113587 + 0.196738i
\(177\) 9.63516 + 4.28985i 0.724223 + 0.322445i
\(178\) 2.04522 6.29454i 0.153296 0.471796i
\(179\) −5.27362 + 16.2305i −0.394169 + 1.21313i 0.535438 + 0.844575i \(0.320147\pi\)
−0.929607 + 0.368553i \(0.879853\pi\)
\(180\) 2.22845 0.431111i 0.166099 0.0321331i
\(181\) −1.44325 + 1.60289i −0.107276 + 0.119142i −0.794391 0.607406i \(-0.792210\pi\)
0.687115 + 0.726548i \(0.258877\pi\)
\(182\) 1.23948 0.0918765
\(183\) −3.67971 11.3250i −0.272012 0.837166i
\(184\) 0.766517 7.29292i 0.0565084 0.537641i
\(185\) 0.409697 0.680478i 0.0301215 0.0500297i
\(186\) −5.13529 2.28638i −0.376538 0.167645i
\(187\) −3.00176 + 1.33647i −0.219511 + 0.0977324i
\(188\) −8.42120 + 3.74936i −0.614179 + 0.273450i
\(189\) −2.14862 + 1.56106i −0.156289 + 0.113551i
\(190\) −1.32289 + 9.65660i −0.0959727 + 0.700564i
\(191\) 9.58826 + 6.96628i 0.693782 + 0.504062i 0.877901 0.478842i \(-0.158943\pi\)
−0.184119 + 0.982904i \(0.558943\pi\)
\(192\) −1.37809 0.292921i −0.0994549 0.0211398i
\(193\) 3.71371 6.43233i 0.267318 0.463009i −0.700850 0.713309i \(-0.747196\pi\)
0.968168 + 0.250300i \(0.0805291\pi\)
\(194\) −5.03176 + 5.58834i −0.361259 + 0.401219i
\(195\) −5.45079 6.28170i −0.390339 0.449842i
\(196\) 6.63142 1.40955i 0.473673 0.100682i
\(197\) 0.398389 1.22611i 0.0283840 0.0873571i −0.935861 0.352369i \(-0.885376\pi\)
0.964245 + 0.265012i \(0.0853761\pi\)
\(198\) 2.47496 1.79817i 0.175888 0.127790i
\(199\) 13.4674 + 23.3262i 0.954679 + 1.65355i 0.735101 + 0.677957i \(0.237135\pi\)
0.219578 + 0.975595i \(0.429532\pi\)
\(200\) −2.33950 4.41891i −0.165428 0.312464i
\(201\) 6.54203 0.461439
\(202\) 1.77331 1.28838i 0.124770 0.0906504i
\(203\) 1.31876 0.280311i 0.0925589 0.0196740i
\(204\) −1.02782 1.14151i −0.0719615 0.0799214i
\(205\) −4.06553 7.34982i −0.283949 0.513334i
\(206\) −5.66372 1.20386i −0.394610 0.0838770i
\(207\) −3.72181 + 6.44636i −0.258684 + 0.448053i
\(208\) −0.815806 2.51079i −0.0565659 0.174092i
\(209\) 3.89570 + 12.5459i 0.269471 + 0.867819i
\(210\) 1.18046 + 0.891186i 0.0814593 + 0.0614977i
\(211\) 0.576741 + 5.48732i 0.0397045 + 0.377763i 0.996273 + 0.0862554i \(0.0274901\pi\)
−0.956569 + 0.291507i \(0.905843\pi\)
\(212\) 7.04381 3.13611i 0.483771 0.215389i
\(213\) −1.19187 + 11.3399i −0.0816656 + 0.776996i
\(214\) −1.60384 15.2596i −0.109637 1.04312i
\(215\) 1.33186 + 0.622501i 0.0908323 + 0.0424542i
\(216\) 4.57639 + 3.32494i 0.311384 + 0.226234i
\(217\) 0.578869 + 1.78158i 0.0392962 + 0.120941i
\(218\) 5.25530 + 9.10244i 0.355934 + 0.616495i
\(219\) 11.0159 12.2344i 0.744385 0.826723i
\(220\) −5.37844 4.06045i −0.362614 0.273755i
\(221\) 0.889445 2.73743i 0.0598305 0.184139i
\(222\) 0.489522 0.104051i 0.0328546 0.00698346i
\(223\) −0.612739 5.82982i −0.0410321 0.390394i −0.995694 0.0927016i \(-0.970450\pi\)
0.954662 0.297692i \(-0.0962169\pi\)
\(224\) 0.234750 + 0.406599i 0.0156849 + 0.0271670i
\(225\) 0.345032 + 5.06362i 0.0230021 + 0.337575i
\(226\) 5.45367 9.44603i 0.362773 0.628341i
\(227\) 13.5308 9.83070i 0.898071 0.652487i −0.0398990 0.999204i \(-0.512704\pi\)
0.937970 + 0.346717i \(0.112704\pi\)
\(228\) −5.01509 + 3.54436i −0.332132 + 0.234731i
\(229\) 4.40388 13.5538i 0.291017 0.895657i −0.693514 0.720443i \(-0.743938\pi\)
0.984530 0.175214i \(-0.0560616\pi\)
\(230\) 15.9737 + 3.70280i 1.05328 + 0.244155i
\(231\) 1.94996 + 0.414477i 0.128298 + 0.0272706i
\(232\) −1.43581 2.48689i −0.0942653 0.163272i
\(233\) 3.91659 + 0.832496i 0.256584 + 0.0545386i 0.334408 0.942429i \(-0.391464\pi\)
−0.0778236 + 0.996967i \(0.524797\pi\)
\(234\) −0.280115 + 2.66511i −0.0183117 + 0.174224i
\(235\) −6.00895 19.7171i −0.391981 1.28620i
\(236\) −6.05639 + 4.40023i −0.394238 + 0.286430i
\(237\) 0.775085 7.37444i 0.0503472 0.479021i
\(238\) −0.0535060 + 0.509076i −0.00346828 + 0.0329985i
\(239\) 2.91818 2.12018i 0.188761 0.137143i −0.489391 0.872064i \(-0.662781\pi\)
0.678152 + 0.734921i \(0.262781\pi\)
\(240\) 1.02830 2.97779i 0.0663764 0.192216i
\(241\) −1.82879 + 17.3997i −0.117803 + 1.12082i 0.762693 + 0.646761i \(0.223877\pi\)
−0.880495 + 0.474055i \(0.842790\pi\)
\(242\) 1.87515 + 0.398574i 0.120539 + 0.0256213i
\(243\) −5.01616 8.68825i −0.321787 0.557352i
\(244\) 8.26728 + 1.75727i 0.529259 + 0.112497i
\(245\) 1.30781 + 15.1031i 0.0835530 + 0.964899i
\(246\) 1.63536 5.03312i 0.104267 0.320900i
\(247\) −10.4505 4.81766i −0.664949 0.306541i
\(248\) 3.22790 2.34521i 0.204972 0.148921i
\(249\) −1.97640 + 3.42323i −0.125249 + 0.216938i
\(250\) 10.4484 3.97881i 0.660815 0.251642i
\(251\) −9.20391 15.9416i −0.580946 1.00623i −0.995368 0.0961426i \(-0.969350\pi\)
0.414422 0.910085i \(-0.363984\pi\)
\(252\) −0.0498159 0.473966i −0.00313810 0.0298571i
\(253\) 21.6175 4.59494i 1.35908 0.288881i
\(254\) −1.31810 + 4.05669i −0.0827049 + 0.254539i
\(255\) 2.81530 1.96756i 0.176301 0.123214i
\(256\) 0.669131 0.743145i 0.0418207 0.0464466i
\(257\) 4.46392 + 7.73173i 0.278452 + 0.482292i 0.971000 0.239079i \(-0.0768455\pi\)
−0.692549 + 0.721371i \(0.743512\pi\)
\(258\) 0.286242 + 0.880963i 0.0178207 + 0.0548464i
\(259\) −0.134924 0.0980280i −0.00838377 0.00609117i
\(260\) 5.79577 1.12123i 0.359438 0.0695360i
\(261\) 0.304690 + 2.89893i 0.0188598 + 0.179439i
\(262\) 1.07867 10.2628i 0.0666401 0.634039i
\(263\) −0.123617 + 0.0550377i −0.00762253 + 0.00339377i −0.410544 0.911841i \(-0.634661\pi\)
0.402922 + 0.915234i \(0.367995\pi\)
\(264\) −0.443834 4.22280i −0.0273161 0.259895i
\(265\) 5.02611 + 16.4921i 0.308752 + 1.01310i
\(266\) 1.99604 + 0.451646i 0.122385 + 0.0276922i
\(267\) 2.88146 + 8.86822i 0.176342 + 0.542726i
\(268\) −2.32172 + 4.02134i −0.141822 + 0.245643i
\(269\) 1.38225 + 0.293807i 0.0842775 + 0.0179137i 0.249857 0.968283i \(-0.419616\pi\)
−0.165580 + 0.986196i \(0.552950\pi\)
\(270\) −8.63471 + 9.24310i −0.525492 + 0.562517i
\(271\) 19.6696 + 21.8453i 1.19484 + 1.32701i 0.932126 + 0.362134i \(0.117952\pi\)
0.262716 + 0.964873i \(0.415382\pi\)
\(272\) 1.06644 0.226679i 0.0646625 0.0137444i
\(273\) −1.41277 + 1.02643i −0.0855045 + 0.0621226i
\(274\) 16.8121 1.01566
\(275\) 10.4871 10.8211i 0.632393 0.652535i
\(276\) 5.16570 + 8.94726i 0.310939 + 0.538562i
\(277\) −7.34880 + 5.33922i −0.441547 + 0.320802i −0.786249 0.617910i \(-0.787980\pi\)
0.344703 + 0.938712i \(0.387980\pi\)
\(278\) 4.87863 15.0149i 0.292601 0.900533i
\(279\) −3.96154 + 0.842051i −0.237171 + 0.0504123i
\(280\) −0.966742 + 0.409343i −0.0577739 + 0.0244629i
\(281\) 2.56106 2.84435i 0.152780 0.169680i −0.661896 0.749596i \(-0.730248\pi\)
0.814676 + 0.579916i \(0.196915\pi\)
\(282\) 6.49361 11.2473i 0.386689 0.669765i
\(283\) 22.8170 + 4.84991i 1.35633 + 0.288297i 0.827994 0.560737i \(-0.189482\pi\)
0.528338 + 0.849034i \(0.322815\pi\)
\(284\) −6.54756 4.75708i −0.388526 0.282281i
\(285\) −6.48894 12.1021i −0.384372 0.716869i
\(286\) 6.43689 4.67667i 0.380621 0.276537i
\(287\) −1.61111 + 0.717312i −0.0951007 + 0.0423416i
\(288\) −0.927315 + 0.412867i −0.0546426 + 0.0243284i
\(289\) −14.4444 6.43104i −0.849668 0.378297i
\(290\) 5.91290 2.50367i 0.347218 0.147021i
\(291\) 1.10743 10.5365i 0.0649186 0.617660i
\(292\) 3.61093 + 11.1133i 0.211314 + 0.650356i
\(293\) −11.3001 −0.660158 −0.330079 0.943953i \(-0.607075\pi\)
−0.330079 + 0.943953i \(0.607075\pi\)
\(294\) −6.39124 + 7.09819i −0.372745 + 0.413975i
\(295\) −8.10243 14.6479i −0.471741 0.852832i
\(296\) −0.109769 + 0.337833i −0.00638017 + 0.0196361i
\(297\) −5.26820 + 16.2138i −0.305692 + 0.940822i
\(298\) 15.2030 + 6.76880i 0.880685 + 0.392106i
\(299\) −9.67969 + 16.7657i −0.559791 + 0.969586i
\(300\) 6.32594 + 3.09931i 0.365228 + 0.178939i
\(301\) 0.154342 0.267329i 0.00889614 0.0154086i
\(302\) −0.433272 4.12231i −0.0249320 0.237212i
\(303\) −0.954292 + 2.93701i −0.0548226 + 0.168727i
\(304\) −0.398874 4.34061i −0.0228770 0.248951i
\(305\) −6.16887 + 17.8641i −0.353228 + 1.02289i
\(306\) −1.08251 0.230096i −0.0618833 0.0131537i
\(307\) 12.6461 21.9037i 0.721752 1.25011i −0.238545 0.971131i \(-0.576670\pi\)
0.960297 0.278980i \(-0.0899963\pi\)
\(308\) −0.946805 + 1.05153i −0.0539492 + 0.0599167i
\(309\) 7.45247 3.31805i 0.423956 0.188757i
\(310\) 4.31838 + 7.80693i 0.245268 + 0.443404i
\(311\) 22.2712 16.1809i 1.26288 0.917537i 0.263986 0.964527i \(-0.414963\pi\)
0.998895 + 0.0469895i \(0.0149627\pi\)
\(312\) 3.00908 + 2.18623i 0.170356 + 0.123771i
\(313\) 2.51816 23.9587i 0.142335 1.35422i −0.657251 0.753672i \(-0.728281\pi\)
0.799586 0.600552i \(-0.205052\pi\)
\(314\) −16.7243 7.44616i −0.943809 0.420211i
\(315\) 1.06548 + 0.0195460i 0.0600330 + 0.00110129i
\(316\) 4.25794 + 3.09358i 0.239528 + 0.174027i
\(317\) 6.25896 6.95128i 0.351538 0.390423i −0.541278 0.840844i \(-0.682059\pi\)
0.892816 + 0.450421i \(0.148726\pi\)
\(318\) −5.43150 + 9.40764i −0.304583 + 0.527554i
\(319\) 5.79096 6.43151i 0.324231 0.360095i
\(320\) 1.46549 + 1.68889i 0.0819234 + 0.0944116i
\(321\) 14.4647 + 16.0647i 0.807343 + 0.896645i
\(322\) 1.06391 3.27438i 0.0592894 0.182474i
\(323\) 2.42982 4.08422i 0.135199 0.227252i
\(324\) −4.92441 −0.273578
\(325\) 0.897360 + 13.1695i 0.0497766 + 0.730511i
\(326\) −1.56426 + 2.70938i −0.0866363 + 0.150059i
\(327\) −13.5279 6.02300i −0.748094 0.333073i
\(328\) 2.51345 + 2.79147i 0.138782 + 0.154133i
\(329\) −4.23335 + 0.899826i −0.233392 + 0.0496090i
\(330\) 9.49288 + 0.174145i 0.522566 + 0.00958638i
\(331\) −0.308839 0.950509i −0.0169753 0.0522447i 0.942210 0.335023i \(-0.108744\pi\)
−0.959185 + 0.282778i \(0.908744\pi\)
\(332\) −1.40282 2.42976i −0.0769900 0.133351i
\(333\) 0.241270 0.267958i 0.0132215 0.0146840i
\(334\) 2.15550 + 1.56606i 0.117944 + 0.0856911i
\(335\) −8.28672 6.25606i −0.452752 0.341805i
\(336\) −0.604280 0.269043i −0.0329662 0.0146775i
\(337\) 7.00904 3.12063i 0.381807 0.169991i −0.206853 0.978372i \(-0.566322\pi\)
0.588660 + 0.808381i \(0.299656\pi\)
\(338\) 0.630347 5.99735i 0.0342864 0.326213i
\(339\) 1.60630 + 15.2829i 0.0872420 + 0.830053i
\(340\) 0.210317 + 2.42882i 0.0114061 + 0.131721i
\(341\) 9.72823 + 7.06797i 0.526813 + 0.382752i
\(342\) −1.42221 + 4.18980i −0.0769046 + 0.226558i
\(343\) 6.46951 0.349321
\(344\) −0.643108 0.136697i −0.0346740 0.00737019i
\(345\) −21.2733 + 9.00764i −1.14531 + 0.484955i
\(346\) −21.1691 + 4.49962i −1.13806 + 0.241901i
\(347\) −2.37991 2.64316i −0.127760 0.141892i 0.675870 0.737020i \(-0.263768\pi\)
−0.803631 + 0.595128i \(0.797101\pi\)
\(348\) 3.69597 + 1.64555i 0.198125 + 0.0882108i
\(349\) −29.2998 −1.56838 −0.784191 0.620519i \(-0.786922\pi\)
−0.784191 + 0.620519i \(0.786922\pi\)
\(350\) −0.643044 2.25771i −0.0343721 0.120680i
\(351\) −7.46690 12.9330i −0.398553 0.690315i
\(352\) 2.75324 + 1.22582i 0.146748 + 0.0653365i
\(353\) 9.36659 28.8274i 0.498533 1.53433i −0.312844 0.949805i \(-0.601282\pi\)
0.811377 0.584523i \(-0.198718\pi\)
\(354\) 3.25920 10.0308i 0.173225 0.533130i
\(355\) 12.3539 13.2243i 0.655677 0.701875i
\(356\) −6.47385 1.37606i −0.343113 0.0729310i
\(357\) −0.360587 0.624555i −0.0190843 0.0330550i
\(358\) 16.6929 + 3.54818i 0.882245 + 0.187527i
\(359\) −22.6981 + 10.1059i −1.19796 + 0.533367i −0.906088 0.423090i \(-0.860945\pi\)
−0.291874 + 0.956457i \(0.594279\pi\)
\(360\) −0.661686 2.17118i −0.0348739 0.114431i
\(361\) −15.0739 11.5663i −0.793361 0.608751i
\(362\) 1.74497 + 1.26780i 0.0917137 + 0.0666339i
\(363\) −2.46736 + 1.09854i −0.129503 + 0.0576584i
\(364\) −0.129561 1.23269i −0.00679085 0.0646106i
\(365\) −25.6533 + 4.96282i −1.34275 + 0.259766i
\(366\) −10.8783 + 4.84333i −0.568618 + 0.253165i
\(367\) −0.552075 + 0.613142i −0.0288181 + 0.0320057i −0.757382 0.652973i \(-0.773522\pi\)
0.728563 + 0.684978i \(0.240188\pi\)
\(368\) −7.33309 −0.382264
\(369\) −1.17825 3.62629i −0.0613374 0.188777i
\(370\) −0.719575 0.336323i −0.0374089 0.0174846i
\(371\) 3.54093 0.752649i 0.183836 0.0390756i
\(372\) −1.73707 + 5.34615i −0.0900628 + 0.277185i
\(373\) 16.0271 11.6444i 0.829851 0.602922i −0.0896664 0.995972i \(-0.528580\pi\)
0.919517 + 0.393050i \(0.128580\pi\)
\(374\) 1.64292 + 2.84562i 0.0849533 + 0.147143i
\(375\) −8.61421 + 13.1875i −0.444836 + 0.681002i
\(376\) 4.60908 + 7.98316i 0.237695 + 0.411700i
\(377\) 0.792437 + 7.53953i 0.0408126 + 0.388306i
\(378\) 1.77710 + 1.97367i 0.0914043 + 0.101515i
\(379\) −6.22404 + 19.1556i −0.319708 + 0.983959i 0.654065 + 0.756438i \(0.273062\pi\)
−0.973773 + 0.227521i \(0.926938\pi\)
\(380\) 9.74198 + 0.306256i 0.499753 + 0.0157106i
\(381\) −1.85704 5.71537i −0.0951388 0.292807i
\(382\) 5.92587 10.2639i 0.303194 0.525147i
\(383\) 0.900303 + 0.191365i 0.0460033 + 0.00977831i 0.230856 0.972988i \(-0.425847\pi\)
−0.184853 + 0.982766i \(0.559181\pi\)
\(384\) −0.147267 + 1.40116i −0.00751521 + 0.0715025i
\(385\) −2.07364 2.38974i −0.105682 0.121792i
\(386\) −6.78528 3.02100i −0.345362 0.153765i
\(387\) 0.539926 + 0.392279i 0.0274460 + 0.0199407i
\(388\) 6.08369 + 4.42006i 0.308852 + 0.224394i
\(389\) −18.2242 8.11392i −0.924002 0.411392i −0.111111 0.993808i \(-0.535441\pi\)
−0.812891 + 0.582416i \(0.802108\pi\)
\(390\) −5.67752 + 6.07755i −0.287493 + 0.307749i
\(391\) −6.46810 4.69935i −0.327106 0.237656i
\(392\) −2.09500 6.44775i −0.105814 0.325661i
\(393\) 7.26933 + 12.5908i 0.366689 + 0.635124i
\(394\) −1.26104 0.268043i −0.0635303 0.0135038i
\(395\) −8.03386 + 8.59992i −0.404228 + 0.432709i
\(396\) −2.04702 2.27344i −0.102867 0.114245i
\(397\) 24.6272 + 27.3512i 1.23600 + 1.37272i 0.902913 + 0.429823i \(0.141424\pi\)
0.333089 + 0.942896i \(0.391909\pi\)
\(398\) 21.7907 15.8319i 1.09227 0.793581i
\(399\) −2.64911 + 1.13817i −0.132622 + 0.0569797i
\(400\) −4.15016 + 2.78859i −0.207508 + 0.139429i
\(401\) −19.1236 + 33.1230i −0.954985 + 1.65408i −0.220581 + 0.975369i \(0.570795\pi\)
−0.734403 + 0.678713i \(0.762538\pi\)
\(402\) −0.683829 6.50620i −0.0341063 0.324500i
\(403\) −10.3032 + 2.19001i −0.513238 + 0.109092i
\(404\) −1.46669 1.62892i −0.0729704 0.0810418i
\(405\) 1.35166 10.9280i 0.0671646 0.543019i
\(406\) −0.416624 1.28224i −0.0206767 0.0636363i
\(407\) −1.07056 −0.0530655
\(408\) −1.02782 + 1.14151i −0.0508845 + 0.0565129i
\(409\) −1.64467 + 15.6480i −0.0813239 + 0.773745i 0.875528 + 0.483168i \(0.160514\pi\)
−0.956852 + 0.290577i \(0.906153\pi\)
\(410\) −6.88460 + 4.81153i −0.340006 + 0.237624i
\(411\) −19.1625 + 13.9224i −0.945215 + 0.686739i
\(412\) −0.605246 + 5.75853i −0.0298183 + 0.283703i
\(413\) −3.21087 + 1.42957i −0.157996 + 0.0703446i
\(414\) 6.80009 + 3.02759i 0.334206 + 0.148798i
\(415\) 5.77708 2.44616i 0.283586 0.120077i
\(416\) −2.41176 + 1.07379i −0.118246 + 0.0526467i
\(417\) 6.87338 + 21.1541i 0.336591 + 1.03592i
\(418\) 12.0700 5.18576i 0.590362 0.253644i
\(419\) −5.79139 17.8241i −0.282928 0.870762i −0.987012 0.160646i \(-0.948642\pi\)
0.704084 0.710116i \(-0.251358\pi\)
\(420\) 0.762912 1.26715i 0.0372263 0.0618304i
\(421\) 4.54355 + 5.04612i 0.221439 + 0.245933i 0.843620 0.536940i \(-0.180420\pi\)
−0.622181 + 0.782873i \(0.713753\pi\)
\(422\) 5.39698 1.14716i 0.262721 0.0558430i
\(423\) −0.978083 9.30584i −0.0475560 0.452465i
\(424\) −3.85521 6.67741i −0.187225 0.324284i
\(425\) −5.44766 0.199940i −0.264250 0.00969851i
\(426\) 11.4023 0.552446
\(427\) 3.62514 + 1.61401i 0.175433 + 0.0781076i
\(428\) −15.0083 + 3.19012i −0.725454 + 0.154200i
\(429\) −3.46396 + 10.6610i −0.167242 + 0.514716i
\(430\) 0.479873 1.38964i 0.0231415 0.0670142i
\(431\) −3.93503 + 4.37029i −0.189544 + 0.210510i −0.830425 0.557130i \(-0.811902\pi\)
0.640881 + 0.767640i \(0.278569\pi\)
\(432\) 2.82837 4.89887i 0.136080 0.235697i
\(433\) −8.41138 + 9.34178i −0.404225 + 0.448937i −0.910546 0.413408i \(-0.864338\pi\)
0.506321 + 0.862345i \(0.331005\pi\)
\(434\) 1.71131 0.761924i 0.0821454 0.0365735i
\(435\) −4.66621 + 7.75026i −0.223728 + 0.371597i
\(436\) 8.50325 6.17797i 0.407232 0.295871i
\(437\) −21.6972 + 23.4722i −1.03792 + 1.12283i
\(438\) −13.3188 9.67670i −0.636399 0.462371i
\(439\) −4.02982 38.3412i −0.192333 1.82993i −0.485932 0.873997i \(-0.661520\pi\)
0.293599 0.955929i \(-0.405147\pi\)
\(440\) −3.47600 + 5.77341i −0.165712 + 0.275236i
\(441\) −0.719339 + 6.84406i −0.0342543 + 0.325908i
\(442\) −2.81541 0.598433i −0.133915 0.0284646i
\(443\) 3.10481 + 5.37769i 0.147514 + 0.255502i 0.930308 0.366779i \(-0.119540\pi\)
−0.782794 + 0.622281i \(0.786206\pi\)
\(444\) −0.154650 0.475964i −0.00733937 0.0225883i
\(445\) 4.83065 13.9888i 0.228995 0.663132i
\(446\) −5.73384 + 1.21877i −0.271505 + 0.0577102i
\(447\) −22.9338 + 4.87472i −1.08473 + 0.230566i
\(448\) 0.379834 0.275965i 0.0179455 0.0130381i
\(449\) −13.7456 −0.648695 −0.324348 0.945938i \(-0.605145\pi\)
−0.324348 + 0.945938i \(0.605145\pi\)
\(450\) 4.99982 0.872435i 0.235694 0.0411270i
\(451\) −5.66034 + 9.80400i −0.266535 + 0.461652i
\(452\) −9.96435 4.43641i −0.468684 0.208671i
\(453\) 3.90759 + 4.33982i 0.183595 + 0.203903i
\(454\) −11.1912 12.4291i −0.525229 0.583326i
\(455\) 2.77110 + 0.0508353i 0.129911 + 0.00238320i
\(456\) 4.04917 + 4.61713i 0.189620 + 0.216217i
\(457\) −18.6745 −0.873558 −0.436779 0.899569i \(-0.643881\pi\)
−0.436779 + 0.899569i \(0.643881\pi\)
\(458\) −13.9398 2.96300i −0.651366 0.138452i
\(459\) 5.63415 2.50848i 0.262979 0.117086i
\(460\) 2.01280 16.2733i 0.0938474 0.758746i
\(461\) −1.57352 14.9711i −0.0732863 0.697272i −0.968054 0.250741i \(-0.919326\pi\)
0.894768 0.446531i \(-0.147341\pi\)
\(462\) 0.208380 1.98261i 0.00969472 0.0922391i
\(463\) −31.7301 23.0533i −1.47462 1.07138i −0.979241 0.202702i \(-0.935028\pi\)
−0.495383 0.868675i \(-0.664972\pi\)
\(464\) −2.32318 + 1.68789i −0.107851 + 0.0783584i
\(465\) −11.3871 5.32225i −0.528066 0.246813i
\(466\) 0.418541 3.98215i 0.0193885 0.184470i
\(467\) −3.89605 11.9908i −0.180288 0.554869i 0.819548 0.573011i \(-0.194225\pi\)
−0.999835 + 0.0181423i \(0.994225\pi\)
\(468\) 2.67980 0.123874
\(469\) −1.45877 + 1.62013i −0.0673598 + 0.0748106i
\(470\) −18.9810 + 8.03704i −0.875528 + 0.370721i
\(471\) 25.2287 5.36253i 1.16248 0.247093i
\(472\) 5.00919 + 5.56327i 0.230567 + 0.256070i
\(473\) −0.207123 1.97064i −0.00952351 0.0906101i
\(474\) −7.41506 −0.340585
\(475\) −3.35363 + 21.5349i −0.153875 + 0.988090i
\(476\) 0.511880 0.0234620
\(477\) 0.818106 + 7.78375i 0.0374585 + 0.356394i
\(478\) −2.41360 2.68057i −0.110395 0.122607i
\(479\) −30.7971 + 6.54613i −1.40716 + 0.299100i −0.848015 0.529973i \(-0.822202\pi\)
−0.559141 + 0.829073i \(0.688869\pi\)
\(480\) −3.06896 0.711402i −0.140078 0.0324709i
\(481\) 0.627496 0.696905i 0.0286114 0.0317761i
\(482\) 17.4956 0.796902
\(483\) 1.49892 + 4.61319i 0.0682031 + 0.209907i
\(484\) 0.200385 1.90654i 0.00910841 0.0866607i
\(485\) −11.4787 + 12.2874i −0.521219 + 0.557943i
\(486\) −8.11632 + 5.89685i −0.368164 + 0.267487i
\(487\) −25.2272 18.3286i −1.14315 0.830548i −0.155596 0.987821i \(-0.549730\pi\)
−0.987555 + 0.157272i \(0.949730\pi\)
\(488\) 0.883472 8.40568i 0.0399929 0.380507i
\(489\) −0.460729 4.38355i −0.0208349 0.198231i
\(490\) 14.8836 2.87935i 0.672373 0.130076i
\(491\) 28.8183 12.8308i 1.30055 0.579044i 0.364599 0.931165i \(-0.381206\pi\)
0.935955 + 0.352121i \(0.114539\pi\)
\(492\) −5.17649 1.10030i −0.233374 0.0496052i
\(493\) −3.13082 −0.141005
\(494\) −3.69890 + 10.8968i −0.166421 + 0.490271i
\(495\) 5.60700 3.91864i 0.252016 0.176130i
\(496\) −2.66977 2.96508i −0.119876 0.133136i
\(497\) −2.54255 2.82378i −0.114049 0.126664i
\(498\) 3.61107 + 1.60775i 0.161816 + 0.0720450i
\(499\) 7.10710 12.3099i 0.318157 0.551065i −0.661946 0.749551i \(-0.730269\pi\)
0.980104 + 0.198487i \(0.0636026\pi\)
\(500\) −5.04917 9.97526i −0.225806 0.446107i
\(501\) −3.75373 −0.167704
\(502\) −14.8922 + 10.8198i −0.664673 + 0.482913i
\(503\) −6.49622 + 1.38081i −0.289652 + 0.0615674i −0.350446 0.936583i \(-0.613970\pi\)
0.0607941 + 0.998150i \(0.480637\pi\)
\(504\) −0.466163 + 0.0990859i −0.0207645 + 0.00441364i
\(505\) 4.01741 2.80770i 0.178772 0.124941i
\(506\) −6.82941 21.0188i −0.303604 0.934398i
\(507\) 4.24803 + 7.35780i 0.188662 + 0.326771i
\(508\) 4.17225 + 0.886839i 0.185114 + 0.0393471i
\(509\) 2.05043 19.5086i 0.0908839 0.864703i −0.850184 0.526485i \(-0.823509\pi\)
0.941068 0.338217i \(-0.109824\pi\)
\(510\) −2.25106 2.59421i −0.0996788 0.114873i
\(511\) 0.573465 + 5.45615i 0.0253686 + 0.241366i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) −7.31201 23.5480i −0.322833 1.03967i
\(514\) 7.22277 5.24765i 0.318583 0.231464i
\(515\) −12.6130 2.92375i −0.555794 0.128836i
\(516\) 0.846217 0.376760i 0.0372526 0.0165859i
\(517\) −18.5895 + 20.6458i −0.817567 + 0.908000i
\(518\) −0.0833876 + 0.144432i −0.00366384 + 0.00634596i
\(519\) 20.4024 22.6591i 0.895564 0.994625i
\(520\) −1.72091 5.64682i −0.0754671 0.247629i
\(521\) −0.878410 + 2.70347i −0.0384839 + 0.118441i −0.968453 0.249197i \(-0.919833\pi\)
0.929969 + 0.367638i \(0.119833\pi\)
\(522\) 2.85120 0.606041i 0.124794 0.0265257i
\(523\) −17.9524 7.99294i −0.785006 0.349507i −0.0252210 0.999682i \(-0.508029\pi\)
−0.759785 + 0.650175i \(0.774696\pi\)
\(524\) −10.3193 −0.450803
\(525\) 2.60259 + 2.04083i 0.113586 + 0.0890692i
\(526\) 0.0676577 + 0.117186i 0.00295001 + 0.00510957i
\(527\) −0.454704 4.32622i −0.0198072 0.188453i
\(528\) −4.15327 + 0.882805i −0.180748 + 0.0384192i
\(529\) 20.5920 + 22.8697i 0.895303 + 0.994334i
\(530\) 15.8764 6.72248i 0.689627 0.292006i
\(531\) −2.34821 7.22703i −0.101903 0.313627i
\(532\) 0.240528 2.03232i 0.0104282 0.0881123i
\(533\) −3.06440 9.43125i −0.132734 0.408513i
\(534\) 8.51845 3.79266i 0.368629 0.164124i
\(535\) −2.95985 34.1814i −0.127966 1.47779i
\(536\) 4.24200 + 1.88866i 0.183226 + 0.0815777i
\(537\) −21.9649 + 9.77940i −0.947855 + 0.422012i
\(538\) 0.147713 1.40539i 0.00636834 0.0605908i
\(539\) 16.5300 12.0098i 0.711999 0.517297i
\(540\) 10.0950 + 7.62124i 0.434421 + 0.327966i
\(541\) 3.30794 31.4729i 0.142219 1.35313i −0.657818 0.753177i \(-0.728520\pi\)
0.800037 0.599950i \(-0.204813\pi\)
\(542\) 19.6696 21.8453i 0.844881 0.938336i
\(543\) −3.03881 −0.130408
\(544\) −0.336911 1.03690i −0.0144449 0.0444569i
\(545\) 11.3759 + 20.5658i 0.487290 + 0.880942i
\(546\) 1.16849 + 1.29773i 0.0500066 + 0.0555379i
\(547\) −24.2223 + 5.14862i −1.03567 + 0.220139i −0.694222 0.719761i \(-0.744251\pi\)
−0.341450 + 0.939900i \(0.610918\pi\)
\(548\) −1.75734 16.7200i −0.0750699 0.714242i
\(549\) −4.28969 + 7.42996i −0.183079 + 0.317103i
\(550\) −11.8580 9.29850i −0.505627 0.396489i
\(551\) −1.47114 + 12.4303i −0.0626729 + 0.529549i
\(552\) 8.35828 6.07265i 0.355752 0.258469i
\(553\) 1.65344 + 1.83633i 0.0703115 + 0.0780888i
\(554\) 6.07813 + 6.75044i 0.258235 + 0.286799i
\(555\) 1.09869 0.212549i 0.0466367 0.00902222i
\(556\) −15.4426 3.28242i −0.654911 0.139206i
\(557\) 7.38594 + 12.7928i 0.312952 + 0.542049i 0.979000 0.203860i \(-0.0653487\pi\)
−0.666048 + 0.745909i \(0.732015\pi\)
\(558\) 1.25153 + 3.85182i 0.0529816 + 0.163060i
\(559\) 1.40424 + 1.02024i 0.0593930 + 0.0431515i
\(560\) 0.508153 + 0.918658i 0.0214734 + 0.0388204i
\(561\) −4.22911 1.88292i −0.178553 0.0794969i
\(562\) −3.09647 2.24972i −0.130617 0.0948986i
\(563\) 0.856673 + 0.622409i 0.0361044 + 0.0262314i 0.605691 0.795700i \(-0.292897\pi\)
−0.569587 + 0.821931i \(0.692897\pi\)
\(564\) −11.8644 5.28238i −0.499582 0.222428i
\(565\) 12.5801 20.8947i 0.529250 0.879049i
\(566\) 2.43831 23.1990i 0.102490 0.975126i
\(567\) −2.26149 0.480694i −0.0949736 0.0201873i
\(568\) −4.04662 + 7.00894i −0.169792 + 0.294089i
\(569\) 5.17193 + 15.9176i 0.216819 + 0.667299i 0.999019 + 0.0442729i \(0.0140971\pi\)
−0.782201 + 0.623026i \(0.785903\pi\)
\(570\) −11.3576 + 7.71842i −0.475716 + 0.323289i
\(571\) −8.04800 + 24.7692i −0.336799 + 1.03656i 0.629031 + 0.777380i \(0.283452\pi\)
−0.965829 + 0.259179i \(0.916548\pi\)
\(572\) −5.32389 5.91278i −0.222603 0.247226i
\(573\) 1.74538 + 16.6061i 0.0729141 + 0.693732i
\(574\) 0.881789 + 1.52730i 0.0368052 + 0.0637484i
\(575\) 35.5605 + 8.93345i 1.48297 + 0.372551i
\(576\) 0.507536 + 0.879079i 0.0211474 + 0.0366283i
\(577\) 36.1646 26.2751i 1.50555 1.09385i 0.537450 0.843296i \(-0.319388\pi\)
0.968103 0.250553i \(-0.0806124\pi\)
\(578\) −4.88597 + 15.0375i −0.203229 + 0.625476i
\(579\) 10.2356 2.17565i 0.425378 0.0904169i
\(580\) −3.10802 5.61880i −0.129054 0.233308i
\(581\) −0.407053 1.25278i −0.0168874 0.0519741i
\(582\) −10.5945 −0.439157
\(583\) 15.5490 17.2689i 0.643973 0.715205i
\(584\) 10.6750 4.75280i 0.441733 0.196672i
\(585\) −0.735556 + 5.94689i −0.0304115 + 0.245874i
\(586\) 1.18118 + 11.2382i 0.0487941 + 0.464245i
\(587\) −26.4049 + 11.7562i −1.08985 + 0.485232i −0.871378 0.490612i \(-0.836773\pi\)
−0.218470 + 0.975844i \(0.570107\pi\)
\(588\) 7.72738 + 5.61427i 0.318672 + 0.231528i
\(589\) −17.3901 0.227539i −0.716546 0.00937556i
\(590\) −13.7207 + 9.58916i −0.564872 + 0.394779i
\(591\) 1.65931 0.738772i 0.0682548 0.0303890i
\(592\) 0.347456 + 0.0738541i 0.0142804 + 0.00303539i
\(593\) −0.220213 0.381419i −0.00904305 0.0156630i 0.861468 0.507811i \(-0.169545\pi\)
−0.870512 + 0.492148i \(0.836212\pi\)
\(594\) 16.6757 + 3.54453i 0.684212 + 0.145434i
\(595\) −0.140502 + 1.13594i −0.00576002 + 0.0465691i
\(596\) 5.14258 15.8272i 0.210648 0.648308i
\(597\) −11.7265 + 36.0905i −0.479934 + 1.47708i
\(598\) 17.6857 + 7.87417i 0.723221 + 0.321999i
\(599\) 7.47102 + 12.9402i 0.305258 + 0.528722i 0.977319 0.211774i \(-0.0679241\pi\)
−0.672061 + 0.740496i \(0.734591\pi\)
\(600\) 2.42109 6.61525i 0.0988405 0.270066i
\(601\) −2.61920 −0.106840 −0.0534198 0.998572i \(-0.517012\pi\)
−0.0534198 + 0.998572i \(0.517012\pi\)
\(602\) −0.281997 0.125553i −0.0114934 0.00511717i
\(603\) −3.15390 3.50277i −0.128437 0.142644i
\(604\) −4.05444 + 0.861797i −0.164973 + 0.0350660i
\(605\) 4.17590 + 0.967996i 0.169774 + 0.0393546i
\(606\) 3.02067 + 0.642063i 0.122706 + 0.0260820i
\(607\) −26.8794 −1.09100 −0.545500 0.838111i \(-0.683660\pi\)
−0.545500 + 0.838111i \(0.683660\pi\)
\(608\) −4.27514 + 0.850406i −0.173380 + 0.0344885i
\(609\) 1.53671 + 1.11648i 0.0622706 + 0.0452422i
\(610\) 18.4110 + 4.26777i 0.745441 + 0.172797i
\(611\) −2.54380 24.2026i −0.102911 0.979134i
\(612\) −0.115682 + 1.10064i −0.00467615 + 0.0444906i
\(613\) 29.0700 12.9428i 1.17413 0.522754i 0.275427 0.961322i \(-0.411181\pi\)
0.898698 + 0.438568i \(0.144514\pi\)
\(614\) −23.1056 10.2873i −0.932466 0.415161i
\(615\) 3.86259 11.1854i 0.155755 0.451040i
\(616\) 1.14474 + 0.831703i 0.0461229 + 0.0335103i
\(617\) 5.87446 6.52425i 0.236497 0.262656i −0.613200 0.789927i \(-0.710118\pi\)
0.849697 + 0.527271i \(0.176785\pi\)
\(618\) −4.07887 7.06481i −0.164076 0.284188i
\(619\) 3.77839 + 11.6287i 0.151866 + 0.467396i 0.997830 0.0658442i \(-0.0209740\pi\)
−0.845964 + 0.533241i \(0.820974\pi\)
\(620\) 7.31277 5.11077i 0.293688 0.205253i
\(621\) −40.5749 + 8.62445i −1.62821 + 0.346087i
\(622\) −18.4203 20.4578i −0.738586 0.820282i
\(623\) −2.83873 1.26388i −0.113731 0.0506364i
\(624\) 1.85972 3.22112i 0.0744482 0.128948i
\(625\) 23.5226 8.46687i 0.940904 0.338675i
\(626\) −24.0906 −0.962855
\(627\) −9.46298 + 15.9061i −0.377915 + 0.635228i
\(628\) −5.65720 + 17.4111i −0.225747 + 0.694777i
\(629\) 0.259143 + 0.287807i 0.0103327 + 0.0114756i
\(630\) −0.0919340 1.06169i −0.00366274 0.0422986i
\(631\) 32.3700 35.9505i 1.28863 1.43117i 0.443806 0.896123i \(-0.353628\pi\)
0.844823 0.535045i \(-0.179705\pi\)
\(632\) 2.63155 4.55799i 0.104678 0.181307i
\(633\) −5.20151 + 5.77686i −0.206741 + 0.229610i
\(634\) −7.56744 5.49807i −0.300541 0.218356i
\(635\) −3.11324 + 9.01545i −0.123545 + 0.357767i
\(636\) 9.92385 + 4.41838i 0.393506 + 0.175200i
\(637\) −1.87086 + 17.8000i −0.0741261 + 0.705263i
\(638\) −7.00160 5.08696i −0.277196 0.201395i
\(639\) 6.64625 4.82879i 0.262922 0.191024i
\(640\) 1.52645 1.63400i 0.0603382 0.0645895i
\(641\) −26.6732 + 11.8757i −1.05353 + 0.469061i −0.859075 0.511850i \(-0.828960\pi\)
−0.194454 + 0.980912i \(0.562294\pi\)
\(642\) 14.4647 16.0647i 0.570878 0.634024i
\(643\) 1.22051 2.11398i 0.0481320 0.0833671i −0.840956 0.541104i \(-0.818007\pi\)
0.889088 + 0.457737i \(0.151340\pi\)
\(644\) −3.36765 0.715816i −0.132704 0.0282071i
\(645\) 0.603818 + 1.98130i 0.0237753 + 0.0780137i
\(646\) −4.31583 1.98959i −0.169804 0.0782795i
\(647\) 0.337248 1.03794i 0.0132586 0.0408057i −0.944208 0.329349i \(-0.893171\pi\)
0.957467 + 0.288543i \(0.0931708\pi\)
\(648\) 0.514741 + 4.89743i 0.0202209 + 0.192389i
\(649\) −11.2808 + 19.5389i −0.442810 + 0.766970i
\(650\) 13.0035 2.26903i 0.510040 0.0889987i
\(651\) −1.31959 + 2.28560i −0.0517190 + 0.0895799i
\(652\) 2.85805 + 1.27248i 0.111930 + 0.0498343i
\(653\) 0.161632 0.497453i 0.00632516 0.0194668i −0.947844 0.318734i \(-0.896742\pi\)
0.954169 + 0.299267i \(0.0967423\pi\)
\(654\) −4.57596 + 14.0834i −0.178934 + 0.550703i
\(655\) 2.83248 22.9002i 0.110674 0.894787i
\(656\) 2.51345 2.79147i 0.0981336 0.108988i
\(657\) −11.8613 −0.462755
\(658\) 1.33740 + 4.11610i 0.0521374 + 0.160462i
\(659\) −1.82163 + 17.3316i −0.0709605 + 0.675144i 0.899998 + 0.435895i \(0.143568\pi\)
−0.970958 + 0.239249i \(0.923099\pi\)
\(660\) −0.819085 9.45908i −0.0318828 0.368194i
\(661\) 41.0975 + 18.2978i 1.59851 + 0.711701i 0.996244 0.0865961i \(-0.0275990\pi\)
0.602264 + 0.798297i \(0.294266\pi\)
\(662\) −0.913020 + 0.406503i −0.0354855 + 0.0157992i
\(663\) 3.70458 1.64939i 0.143874 0.0640568i
\(664\) −2.26982 + 1.64912i −0.0880860 + 0.0639982i
\(665\) 4.44402 + 1.09160i 0.172332 + 0.0423306i
\(666\) −0.291710 0.211939i −0.0113035 0.00821249i
\(667\) 20.5976 + 4.37816i 0.797543 + 0.169523i
\(668\) 1.33217 2.30739i 0.0515433 0.0892756i
\(669\) 5.52617 6.13744i 0.213654 0.237287i
\(670\) −5.35559 + 8.89526i −0.206904 + 0.343654i
\(671\) 24.9159 5.29604i 0.961868 0.204451i
\(672\) −0.204405 + 0.629092i −0.00788507 + 0.0242678i
\(673\) −5.29074 + 3.84395i −0.203943 + 0.148173i −0.685069 0.728478i \(-0.740228\pi\)
0.481126 + 0.876651i \(0.340228\pi\)
\(674\) −3.83618 6.64445i −0.147764 0.255935i
\(675\) −19.6836 + 20.3106i −0.757624 + 0.781755i
\(676\) −6.03039 −0.231938
\(677\) 2.23331 1.62260i 0.0858331 0.0623614i −0.544041 0.839059i \(-0.683106\pi\)
0.629874 + 0.776697i \(0.283106\pi\)
\(678\) 15.0313 3.19499i 0.577272 0.122703i
\(679\) 2.36241 + 2.62373i 0.0906611 + 0.100689i
\(680\) 2.39353 0.463046i 0.0917877 0.0177570i
\(681\) 23.0485 + 4.89911i 0.883220 + 0.187734i
\(682\) 6.01238 10.4137i 0.230226 0.398763i
\(683\) 11.2977 + 34.7707i 0.432293 + 1.33046i 0.895835 + 0.444387i \(0.146579\pi\)
−0.463541 + 0.886075i \(0.653421\pi\)
\(684\) 4.31551 + 0.976471i 0.165007 + 0.0373363i
\(685\) 37.5866 + 0.689520i 1.43611 + 0.0263452i
\(686\) −0.676248 6.43407i −0.0258193 0.245654i
\(687\) 18.3424 8.16655i 0.699805 0.311573i
\(688\) −0.0687248 + 0.653873i −0.00262011 + 0.0249287i
\(689\) 2.12773 + 20.2440i 0.0810600 + 0.771235i
\(690\) 11.1820 + 20.2152i 0.425690 + 0.769578i
\(691\) 4.62061 + 3.35707i 0.175776 + 0.127709i 0.672195 0.740375i \(-0.265352\pi\)
−0.496418 + 0.868083i \(0.665352\pi\)
\(692\) 6.68774 + 20.5828i 0.254230 + 0.782439i
\(693\) −0.718153 1.24388i −0.0272804 0.0472510i
\(694\) −2.37991 + 2.64316i −0.0903402 + 0.100333i
\(695\) 11.5229 33.3686i 0.437089 1.26574i
\(696\) 1.25020 3.84773i 0.0473888 0.145848i
\(697\) 4.00586 0.851471i 0.151733 0.0322518i
\(698\) 3.06266 + 29.1393i 0.115923 + 1.10294i
\(699\) 2.82063 + 4.88547i 0.106686 + 0.184785i
\(700\) −2.17813 + 0.875516i −0.0823254 + 0.0330914i
\(701\) 25.4051 44.0029i 0.959536 1.66197i 0.235909 0.971775i \(-0.424193\pi\)
0.723627 0.690191i \(-0.242473\pi\)
\(702\) −12.0817 + 8.77786i −0.455994 + 0.331299i
\(703\) 1.26445 0.893638i 0.0476897 0.0337042i
\(704\) 0.931314 2.86629i 0.0351002 0.108027i
\(705\) 14.9790 24.8791i 0.564142 0.937001i
\(706\) −29.6486 6.30200i −1.11584 0.237179i
\(707\) −0.514556 0.891237i −0.0193519 0.0335184i
\(708\) −10.3165 2.19284i −0.387719 0.0824121i
\(709\) −0.272859 + 2.59608i −0.0102474 + 0.0974980i −0.998450 0.0556538i \(-0.982276\pi\)
0.988203 + 0.153152i \(0.0489423\pi\)
\(710\) −14.4432 10.9039i −0.542045 0.409216i
\(711\) −4.32212 + 3.14021i −0.162092 + 0.117767i
\(712\) −0.691819 + 6.58222i −0.0259270 + 0.246679i
\(713\) −3.05833 + 29.0980i −0.114535 + 1.08973i
\(714\) −0.583442 + 0.423896i −0.0218348 + 0.0158639i
\(715\) 14.5827 10.1916i 0.545362 0.381144i
\(716\) 1.78386 16.9723i 0.0666660 0.634285i
\(717\) 4.97085 + 1.05659i 0.185640 + 0.0394590i
\(718\) 12.4231 + 21.5174i 0.463626 + 0.803024i
\(719\) 39.3502 + 8.36414i 1.46751 + 0.311930i 0.871242 0.490853i \(-0.163315\pi\)
0.596271 + 0.802783i \(0.296648\pi\)
\(720\) −2.09012 + 0.885012i −0.0778943 + 0.0329824i
\(721\) −0.840070 + 2.58547i −0.0312859 + 0.0962880i
\(722\) −9.92727 + 16.2003i −0.369455 + 0.602912i
\(723\) −19.9415 + 14.4884i −0.741634 + 0.538828i
\(724\) 1.07845 1.86793i 0.0400804 0.0694212i
\(725\) 13.3221 5.35493i 0.494771 0.198877i
\(726\) 1.35043 + 2.33902i 0.0501192 + 0.0868091i
\(727\) 3.01042 + 28.6422i 0.111650 + 1.06228i 0.896636 + 0.442768i \(0.146003\pi\)
−0.784986 + 0.619514i \(0.787330\pi\)
\(728\) −1.21240 + 0.257703i −0.0449344 + 0.00955110i
\(729\) 8.93291 27.4927i 0.330849 1.01825i
\(730\) 7.61713 + 24.9940i 0.281923 + 0.925069i
\(731\) −0.479648 + 0.532703i −0.0177404 + 0.0197027i
\(732\) 5.95389 + 10.3124i 0.220062 + 0.381159i
\(733\) −4.94484 15.2187i −0.182642 0.562114i 0.817258 0.576272i \(-0.195493\pi\)
−0.999900 + 0.0141583i \(0.995493\pi\)
\(734\) 0.667490 + 0.484960i 0.0246375 + 0.0179002i
\(735\) −14.5800 + 15.6072i −0.537790 + 0.575682i
\(736\) 0.766517 + 7.29292i 0.0282542 + 0.268821i
\(737\) −1.46281 + 13.9177i −0.0538834 + 0.512666i
\(738\) −3.48326 + 1.55085i −0.128221 + 0.0570875i
\(739\) −2.09108 19.8953i −0.0769215 0.731860i −0.963214 0.268734i \(-0.913395\pi\)
0.886293 0.463125i \(-0.153272\pi\)
\(740\) −0.259264 + 0.750789i −0.00953075 + 0.0275995i
\(741\) −4.80782 15.4834i −0.176620 0.568795i
\(742\) −1.11865 3.44286i −0.0410671 0.126391i
\(743\) −15.4635 + 26.7835i −0.567299 + 0.982591i 0.429533 + 0.903051i \(0.358678\pi\)
−0.996832 + 0.0795396i \(0.974655\pi\)
\(744\) 5.49843 + 1.16873i 0.201582 + 0.0428477i
\(745\) 33.7116 + 15.7565i 1.23510 + 0.577273i
\(746\) −13.2559 14.7221i −0.485331 0.539015i
\(747\) 2.78570 0.592119i 0.101924 0.0216645i
\(748\) 2.65830 1.93137i 0.0971970 0.0706178i
\(749\) −7.20383 −0.263222
\(750\) 14.0157 + 7.18855i 0.511782 + 0.262489i
\(751\) −18.0341 31.2360i −0.658075 1.13982i −0.981113 0.193433i \(-0.938038\pi\)
0.323039 0.946386i \(-0.395296\pi\)
\(752\) 7.45764 5.41830i 0.271952 0.197585i
\(753\) 8.01414 24.6650i 0.292052 0.898842i
\(754\) 7.41540 1.57619i 0.270053 0.0574015i
\(755\) −0.799593 9.23398i −0.0291002 0.336059i
\(756\) 1.77710 1.97367i 0.0646326 0.0717818i
\(757\) 25.3716 43.9449i 0.922147 1.59721i 0.126061 0.992022i \(-0.459766\pi\)
0.796086 0.605184i \(-0.206900\pi\)
\(758\) 19.7013 + 4.18764i 0.715583 + 0.152102i
\(759\) 25.1901 + 18.3017i 0.914344 + 0.664310i
\(760\) −0.713736 9.72063i −0.0258899 0.352604i
\(761\) 5.52774 4.01613i 0.200380 0.145585i −0.483070 0.875582i \(-0.660478\pi\)
0.683451 + 0.729997i \(0.260478\pi\)
\(762\) −5.48995 + 2.44428i −0.198880 + 0.0885470i
\(763\) 4.50810 2.00713i 0.163204 0.0726632i
\(764\) −10.8271 4.82054i −0.391711 0.174401i
\(765\) −2.41073 0.558821i −0.0871602 0.0202042i
\(766\) 0.0962097 0.915374i 0.00347620 0.0330738i
\(767\) −6.10721 18.7961i −0.220519 0.678687i
\(768\) 1.40887 0.0508384
\(769\) 7.99608 8.88054i 0.288346 0.320241i −0.581517 0.813534i \(-0.697541\pi\)
0.869863 + 0.493294i \(0.164207\pi\)
\(770\) −2.15989 + 2.31207i −0.0778371 + 0.0833213i
\(771\) −3.88688 + 11.9626i −0.139982 + 0.430822i
\(772\) −2.29520 + 7.06389i −0.0826059 + 0.254235i
\(773\) −35.9206 15.9929i −1.29197 0.575224i −0.358386 0.933574i \(-0.616673\pi\)
−0.933587 + 0.358350i \(0.883339\pi\)
\(774\) 0.333692 0.577972i 0.0119943 0.0207748i
\(775\) 9.33438 + 17.6310i 0.335301 + 0.633325i
\(776\) 3.75992 6.51238i 0.134973 0.233781i
\(777\) −0.0245606 0.233678i −0.000881106 0.00838316i
\(778\) −6.16453 + 18.9725i −0.221009 + 0.680196i
\(779\) −1.49828 16.3046i −0.0536816 0.584172i
\(780\) 6.63772 + 5.01114i 0.237668 + 0.179428i
\(781\) −23.8583 5.07125i −0.853718 0.181463i
\(782\) −3.99751 + 6.92389i −0.142951 + 0.247598i
\(783\) −10.8693 + 12.0716i −0.388438 + 0.431404i
\(784\) −6.19344 + 2.75750i −0.221194 + 0.0984821i
\(785\) −37.0851 17.3332i −1.32362 0.618650i
\(786\) 11.7620 8.54561i 0.419537 0.304812i
\(787\) −26.7158 19.4101i −0.952314 0.691896i −0.000960833 1.00000i \(-0.500306\pi\)
−0.951353 + 0.308103i \(0.900306\pi\)
\(788\) −0.134759 + 1.28215i −0.00480061 + 0.0456747i
\(789\) −0.174160 0.0775412i −0.00620027 0.00276054i
\(790\) 9.39257 + 7.09092i 0.334173 + 0.252284i
\(791\) −4.14297 3.01005i −0.147307 0.107025i
\(792\) −2.04702 + 2.27344i −0.0727377 + 0.0807833i
\(793\) −11.1566 + 19.3238i −0.396183 + 0.686210i
\(794\) 24.6272 27.3512i 0.873985 0.970659i
\(795\) −12.5290 + 20.8098i −0.444358 + 0.738048i
\(796\) −18.0229 20.0165i −0.638805 0.709465i
\(797\) 11.6483 35.8499i 0.412605 1.26987i −0.501770 0.865001i \(-0.667318\pi\)
0.914375 0.404867i \(-0.132682\pi\)
\(798\) 1.40884 + 2.51563i 0.0498725 + 0.0890523i
\(799\) 10.0502 0.355552
\(800\) 3.20712 + 3.83593i 0.113389 + 0.135621i
\(801\) 3.35912 5.81816i 0.118689 0.205575i
\(802\) 34.9405 + 15.5565i 1.23379 + 0.549319i
\(803\) 23.5647 + 26.1712i 0.831579 + 0.923562i
\(804\) −6.39907 + 1.36017i −0.225678 + 0.0479693i
\(805\) 2.51287 7.27687i 0.0885670 0.256476i
\(806\) 3.25499 + 10.0178i 0.114652 + 0.352862i
\(807\) 0.995464 + 1.72419i 0.0350420 + 0.0606945i
\(808\) −1.46669 + 1.62892i −0.0515979 + 0.0573052i
\(809\) 6.27738 + 4.56079i 0.220701 + 0.160349i 0.692642 0.721281i \(-0.256447\pi\)
−0.471941 + 0.881630i \(0.656447\pi\)
\(810\) −11.0095 0.201967i −0.386833 0.00709638i
\(811\) −13.8701 6.17537i −0.487045 0.216846i 0.148497 0.988913i \(-0.452557\pi\)
−0.635542 + 0.772066i \(0.719223\pi\)
\(812\) −1.23166 + 0.548371i −0.0432229 + 0.0192441i
\(813\) −4.32904 + 41.1880i −0.151826 + 1.44453i
\(814\) 0.111904 + 1.06469i 0.00392222 + 0.0373174i
\(815\) −3.60832 + 5.99318i −0.126394 + 0.209932i
\(816\) 1.24269 + 0.902866i 0.0435028 + 0.0316066i
\(817\) 1.88961 + 2.15466i 0.0661091 + 0.0753820i
\(818\) 15.7342 0.550134
\(819\) 1.23067 + 0.261587i 0.0430031 + 0.00914059i
\(820\) 5.50480 + 6.34394i 0.192236 + 0.221540i
\(821\) 3.02467 0.642913i 0.105562 0.0224378i −0.154828 0.987941i \(-0.549482\pi\)
0.260390 + 0.965504i \(0.416149\pi\)
\(822\) 15.8491 + 17.6022i 0.552801 + 0.613948i
\(823\) −23.0863 10.2787i −0.804739 0.358293i −0.0372103 0.999307i \(-0.511847\pi\)
−0.767529 + 0.641015i \(0.778514\pi\)
\(824\) 5.79025 0.201713
\(825\) 21.2160 + 0.778670i 0.738647 + 0.0271098i
\(826\) 1.75737 + 3.04385i 0.0611466 + 0.105909i
\(827\) 44.0218 + 19.5998i 1.53079 + 0.681551i 0.987446 0.157960i \(-0.0504917\pi\)
0.543343 + 0.839511i \(0.317158\pi\)
\(828\) 2.30021 7.07930i 0.0799377 0.246023i
\(829\) 10.3717 31.9207i 0.360223 1.10865i −0.592696 0.805426i \(-0.701936\pi\)
0.952919 0.303226i \(-0.0980636\pi\)
\(830\) −3.03663 5.48973i −0.105403 0.190551i
\(831\) −12.5180 2.66079i −0.434245 0.0923017i
\(832\) 1.32000 + 2.28631i 0.0457628 + 0.0792635i
\(833\) −7.23001 1.53679i −0.250505 0.0532465i
\(834\) 20.3197 9.04693i 0.703615 0.313269i
\(835\) 4.75480 + 3.58964i 0.164547 + 0.124225i
\(836\) −6.41901 11.4618i −0.222006 0.396414i
\(837\) −18.2594 13.2662i −0.631136 0.458547i
\(838\) −17.1210 + 7.62278i −0.591437 + 0.263325i
\(839\) −2.37453 22.5921i −0.0819778 0.779967i −0.955859 0.293827i \(-0.905071\pi\)
0.873881 0.486140i \(-0.161596\pi\)
\(840\) −1.33995 0.626280i −0.0462327 0.0216087i
\(841\) −18.9596 + 8.44135i −0.653779 + 0.291081i
\(842\) 4.54355 5.04612i 0.156581 0.173901i
\(843\) 5.39240 0.185724
\(844\) −1.70502 5.24750i −0.0586891 0.180626i
\(845\) 1.65523 13.3824i 0.0569418 0.460368i
\(846\) −9.15262 + 1.94545i −0.314674 + 0.0668860i
\(847\) 0.278131 0.855998i 0.00955668 0.0294124i
\(848\) −6.23785 + 4.53207i −0.214209 + 0.155632i
\(849\) 16.4323 + 28.4615i 0.563953 + 0.976796i
\(850\) 0.370591 + 5.43872i 0.0127112 + 0.186546i
\(851\) −1.30243 2.25587i −0.0446466 0.0773301i
\(852\) −1.19187 11.3399i −0.0408328 0.388498i
\(853\) 2.26724 + 2.51803i 0.0776290 + 0.0862157i 0.780708 0.624896i \(-0.214859\pi\)
−0.703079 + 0.711112i \(0.748192\pi\)
\(854\) 1.22624 3.77399i 0.0419612 0.129143i
\(855\) −3.35147 + 9.30876i −0.114618 + 0.318353i
\(856\) 4.74144 + 14.5926i 0.162059 + 0.498766i
\(857\) −20.5375 + 35.5720i −0.701547 + 1.21512i 0.266376 + 0.963869i \(0.414174\pi\)
−0.967923 + 0.251246i \(0.919160\pi\)
\(858\) 10.9647 + 2.33061i 0.374327 + 0.0795657i
\(859\) −0.906358 + 8.62342i −0.0309245 + 0.294227i 0.968119 + 0.250492i \(0.0805924\pi\)
−0.999043 + 0.0437351i \(0.986074\pi\)
\(860\) −1.43218 0.331988i −0.0488371 0.0113207i
\(861\) −2.26985 1.01060i −0.0773563 0.0344412i
\(862\) 4.75768 + 3.45665i 0.162047 + 0.117734i
\(863\) 33.4630 + 24.3123i 1.13909 + 0.827601i 0.986993 0.160764i \(-0.0513958\pi\)
0.152102 + 0.988365i \(0.451396\pi\)
\(864\) −5.16768 2.30080i −0.175808 0.0782748i
\(865\) −47.5120 + 9.19156i −1.61546 + 0.312522i
\(866\) 10.1698 + 7.38882i 0.345585 + 0.251082i
\(867\) −6.88371 21.1859i −0.233783 0.719511i
\(868\) −0.936630 1.62229i −0.0317913 0.0550641i
\(869\) 15.5153 + 3.29788i 0.526321 + 0.111873i
\(870\) 8.19556 + 3.83053i 0.277855 + 0.129867i
\(871\) −8.20268 9.11000i −0.277937 0.308681i
\(872\) −7.03296 7.81090i −0.238166 0.264510i
\(873\) −6.17538 + 4.48668i −0.209005 + 0.151851i
\(874\) 25.6116 + 19.1248i 0.866324 + 0.646906i
\(875\) −1.34505 5.07392i −0.0454710 0.171530i
\(876\) −8.23150 + 14.2574i −0.278116 + 0.481712i
\(877\) 1.24094 + 11.8068i 0.0419037 + 0.398687i 0.995291 + 0.0969366i \(0.0309044\pi\)
−0.953387 + 0.301751i \(0.902429\pi\)
\(878\) −37.7099 + 8.01549i −1.27265 + 0.270510i
\(879\) −10.6528 11.8312i −0.359311 0.399055i
\(880\) 6.10512 + 2.85348i 0.205804 + 0.0961907i
\(881\) −11.2289 34.5590i −0.378311 1.16432i −0.941218 0.337801i \(-0.890317\pi\)
0.562907 0.826521i \(-0.309683\pi\)
\(882\) 6.88176 0.231721
\(883\) 2.08590 2.31662i 0.0701960 0.0779605i −0.707024 0.707190i \(-0.749963\pi\)
0.777220 + 0.629229i \(0.216629\pi\)
\(884\) −0.300865 + 2.86254i −0.0101192 + 0.0962775i
\(885\) 7.69797 22.2921i 0.258764 0.749340i
\(886\) 5.02369 3.64992i 0.168774 0.122622i
\(887\) −2.93063 + 27.8831i −0.0984008 + 0.936221i 0.828265 + 0.560336i \(0.189328\pi\)
−0.926666 + 0.375885i \(0.877339\pi\)
\(888\) −0.457192 + 0.203555i −0.0153423 + 0.00683085i
\(889\) 1.82950 + 0.814544i 0.0613594 + 0.0273189i
\(890\) −14.4171 3.34196i −0.483262 0.112023i
\(891\) −13.5581 + 6.03644i −0.454213 + 0.202228i
\(892\) 1.81144 + 5.57503i 0.0606514 + 0.186666i
\(893\) 4.72252 39.9025i 0.158033 1.33529i
\(894\) 7.24525 + 22.2986i 0.242317 + 0.745776i
\(895\) 37.1746 + 8.61726i 1.24261 + 0.288043i
\(896\) −0.314157 0.348907i −0.0104952 0.0116562i
\(897\) −26.6789 + 5.67078i −0.890783 + 0.189342i
\(898\) 1.43681 + 13.6703i 0.0479469 + 0.456184i
\(899\) 5.72873 + 9.92245i 0.191064 + 0.330932i
\(900\) −1.39028 4.88123i −0.0463426 0.162708i
\(901\) −8.40640 −0.280058
\(902\) 10.3420 + 4.60454i 0.344349 + 0.153314i
\(903\) 0.425394 0.0904204i 0.0141562 0.00300900i
\(904\) −3.37055 + 10.3735i −0.112103 + 0.345017i
\(905\) 3.84922 + 2.90597i 0.127953 + 0.0965977i
\(906\) 3.90759 4.33982i 0.129821 0.144181i
\(907\) 22.8276 39.5386i 0.757979 1.31286i −0.185900 0.982569i \(-0.559520\pi\)
0.943880 0.330290i \(-0.107146\pi\)
\(908\) −11.1912 + 12.4291i −0.371393 + 0.412474i
\(909\) 2.03261 0.904976i 0.0674174 0.0300162i
\(910\) −0.239102 2.76123i −0.00792615 0.0915340i
\(911\) 15.8495 11.5153i 0.525117 0.381520i −0.293411 0.955986i \(-0.594791\pi\)
0.818528 + 0.574467i \(0.194791\pi\)
\(912\) 4.16858 4.50960i 0.138036 0.149328i
\(913\) −6.84076 4.97011i −0.226396 0.164487i
\(914\) 1.95202 + 18.5722i 0.0645671 + 0.614315i
\(915\) −24.5192 + 10.3820i −0.810578 + 0.343220i
\(916\) −1.48966 + 14.1732i −0.0492198 + 0.468295i
\(917\) −4.73906 1.00732i −0.156498 0.0332646i
\(918\) −3.08367 5.34107i −0.101776 0.176282i
\(919\) 1.64171 + 5.05267i 0.0541550 + 0.166672i 0.974476 0.224492i \(-0.0720724\pi\)
−0.920321 + 0.391164i \(0.872072\pi\)
\(920\) −16.3945 0.300755i −0.540512 0.00991559i
\(921\) 34.8549 7.40864i 1.14851 0.244123i
\(922\) −14.7246 + 3.12981i −0.484928 + 0.103075i
\(923\) 17.2856 12.5587i 0.568962 0.413375i
\(924\) −1.99353 −0.0655822
\(925\) −1.59495 0.781427i −0.0524418 0.0256932i
\(926\) −19.6103 + 33.9660i −0.644434 + 1.11619i
\(927\) −5.36939 2.39061i −0.176354 0.0785178i
\(928\) 1.92148 + 2.13402i 0.0630758 + 0.0700528i
\(929\) −22.4117 24.8907i −0.735303 0.816637i 0.253268 0.967396i \(-0.418495\pi\)
−0.988570 + 0.150760i \(0.951828\pi\)
\(930\) −4.10281 + 11.8811i −0.134537 + 0.389596i
\(931\) −9.49883 + 27.9832i −0.311312 + 0.917113i
\(932\) −4.00408 −0.131158
\(933\) 37.9369 + 8.06374i 1.24200 + 0.263995i
\(934\) −11.5179 + 5.12809i −0.376877 + 0.167796i
\(935\) 3.55635 + 6.42931i 0.116305 + 0.210261i
\(936\) −0.280115 2.66511i −0.00915584 0.0871120i
\(937\) −2.85453 + 27.1591i −0.0932536 + 0.887249i 0.843469 + 0.537177i \(0.180509\pi\)
−0.936723 + 0.350071i \(0.886157\pi\)
\(938\) 1.76374 + 1.28143i 0.0575881 + 0.0418402i
\(939\) 27.4586 19.9498i 0.896077 0.651038i
\(940\) 9.97706 + 18.0369i 0.325416 + 0.588299i
\(941\) −1.66138 + 15.8070i −0.0541596 + 0.515294i 0.933489 + 0.358607i \(0.116748\pi\)
−0.987648 + 0.156687i \(0.949919\pi\)
\(942\) −7.97028 24.5300i −0.259686 0.799230i
\(943\) −27.5452 −0.896995
\(944\) 5.00919 5.56327i 0.163035 0.181069i
\(945\) 3.89211 + 4.48541i 0.126610 + 0.145910i
\(946\) −1.93819 + 0.411976i −0.0630161 + 0.0133945i
\(947\) 4.08012 + 4.53144i 0.132586 + 0.147252i 0.805782 0.592213i \(-0.201745\pi\)
−0.673196 + 0.739465i \(0.735079\pi\)
\(948\) 0.775085 + 7.37444i 0.0251736 + 0.239511i
\(949\) −30.8490 −1.00140
\(950\) 21.7675 + 1.08425i 0.706231 + 0.0351776i
\(951\) 13.1784 0.427340
\(952\) −0.0535060 0.509076i −0.00173414 0.0164992i
\(953\) 25.1621 + 27.9453i 0.815081 + 0.905239i 0.996947 0.0780846i \(-0.0248804\pi\)
−0.181866 + 0.983323i \(0.558214\pi\)
\(954\) 7.65560 1.62725i 0.247859 0.0526841i
\(955\) 13.6694 22.7039i 0.442331 0.734681i
\(956\) −2.41360 + 2.68057i −0.0780614 + 0.0866959i
\(957\) 12.1930 0.394145
\(958\) 9.72944 + 29.9441i 0.314344 + 0.967451i
\(959\) 0.825072 7.85004i 0.0266430 0.253491i
\(960\) −0.386711 + 3.12651i −0.0124810 + 0.100908i
\(961\) 12.2005 8.86420i 0.393565 0.285942i
\(962\) −0.758679 0.551212i −0.0244608 0.0177718i
\(963\) 1.62802 15.4896i 0.0524622 0.499144i
\(964\) −1.82879 17.3997i −0.0589013 0.560408i
\(965\) −15.0459 7.03231i −0.484344 0.226378i
\(966\) 4.43124 1.97292i 0.142573 0.0634775i
\(967\) 13.5778 + 2.88606i 0.436634 + 0.0928093i 0.420984 0.907068i \(-0.361685\pi\)
0.0156498 + 0.999878i \(0.495018\pi\)
\(968\) −1.91704 −0.0616159
\(969\) 6.56681 1.30626i 0.210956 0.0419632i
\(970\) 13.4200 + 10.1314i 0.430889 + 0.325300i
\(971\) 3.69258 + 4.10103i 0.118501 + 0.131608i 0.799476 0.600698i \(-0.205111\pi\)
−0.680975 + 0.732306i \(0.738444\pi\)
\(972\) 6.71294 + 7.45547i 0.215318 + 0.239134i
\(973\) −6.77145 3.01484i −0.217083 0.0966514i
\(974\) −15.5912 + 27.0048i −0.499576 + 0.865290i
\(975\) −12.9425 + 13.3547i −0.414490 + 0.427692i
\(976\) −8.45198 −0.270541
\(977\) −10.8157 + 7.85808i −0.346026 + 0.251402i −0.747200 0.664599i \(-0.768602\pi\)
0.401174 + 0.916002i \(0.368602\pi\)
\(978\) −4.31137 + 0.916411i −0.137863 + 0.0293036i
\(979\) −19.5108 + 4.14716i −0.623569 + 0.132544i
\(980\) −4.41934 14.5011i −0.141170 0.463221i
\(981\) 3.29691 + 10.1468i 0.105262 + 0.323964i
\(982\) −15.7728 27.3193i −0.503330 0.871794i
\(983\) −33.5322 7.12749i −1.06951 0.227332i −0.360666 0.932695i \(-0.617451\pi\)
−0.708846 + 0.705363i \(0.750784\pi\)
\(984\) −0.553179 + 5.26315i −0.0176347 + 0.167783i
\(985\) −2.80831 0.650980i −0.0894801 0.0207419i
\(986\) 0.327260 + 3.11367i 0.0104221 + 0.0991594i
\(987\) −4.93298 3.58402i −0.157019 0.114081i
\(988\) 11.2238 + 2.53961i 0.357076 + 0.0807956i
\(989\) 3.90053 2.83390i 0.124030 0.0901128i
\(990\) −4.48326 5.16668i −0.142487 0.164208i
\(991\) −26.3346 + 11.7249i −0.836547 + 0.372455i −0.779873 0.625938i \(-0.784716\pi\)
−0.0566744 + 0.998393i \(0.518050\pi\)
\(992\) −2.66977 + 2.96508i −0.0847652 + 0.0941412i
\(993\) 0.704032 1.21942i 0.0223418 0.0386971i
\(994\) −2.54255 + 2.82378i −0.0806446 + 0.0895649i
\(995\) 49.3666 34.5015i 1.56503 1.09377i
\(996\) 1.22148 3.75934i 0.0387042 0.119119i
\(997\) −20.1703 + 4.28733i −0.638800 + 0.135781i −0.515915 0.856640i \(-0.672548\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(998\) −12.9853 5.78143i −0.411043 0.183008i
\(999\) 2.00938 0.0635739
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 950.2.r.b.11.19 200
19.7 even 3 inner 950.2.r.b.311.7 yes 200
25.16 even 5 inner 950.2.r.b.391.7 yes 200
475.216 even 15 inner 950.2.r.b.691.19 yes 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.r.b.11.19 200 1.1 even 1 trivial
950.2.r.b.311.7 yes 200 19.7 even 3 inner
950.2.r.b.391.7 yes 200 25.16 even 5 inner
950.2.r.b.691.19 yes 200 475.216 even 15 inner