Properties

Label 315.2.i.d.106.4
Level $315$
Weight $2$
Character 315.106
Analytic conductor $2.515$
Analytic rank $0$
Dimension $8$
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] = [315,2,Mod(106,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.i (of order \(3\), degree \(2\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 106.4
Root \(-0.978148 - 0.207912i\) of defining polynomial
Character \(\chi\) \(=\) 315.106
Dual form 315.2.i.d.211.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.913545 - 1.58231i) q^{2} +(0.360114 + 1.69420i) q^{3} +(-0.669131 - 1.15897i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.00973 + 0.977920i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.20906 q^{8} +(-2.74064 + 1.22021i) q^{9} +O(q^{10})\) \(q+(0.913545 - 1.58231i) q^{2} +(0.360114 + 1.69420i) q^{3} +(-0.669131 - 1.15897i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.00973 + 0.977920i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.20906 q^{8} +(-2.74064 + 1.22021i) q^{9} +1.82709 q^{10} +(-0.0864545 + 0.149744i) q^{11} +(1.72256 - 1.55100i) q^{12} +(1.87362 + 3.24520i) q^{13} +(-0.913545 - 1.58231i) q^{14} +(-1.28716 + 1.15897i) q^{15} +(2.44279 - 4.23104i) q^{16} +1.82709 q^{17} +(-0.572949 + 5.45125i) q^{18} -0.138341 q^{19} +(0.669131 - 1.15897i) q^{20} +(1.64728 + 0.535233i) q^{21} +(0.157960 + 0.273595i) q^{22} +(-3.90142 - 6.75746i) q^{23} +(0.435398 + 2.04839i) q^{24} +(-0.500000 + 0.866025i) q^{25} +6.84655 q^{26} +(-3.05422 - 4.20378i) q^{27} -1.33826 q^{28} +(0.489318 - 0.847523i) q^{29} +(0.657960 + 3.09546i) q^{30} +(1.36245 + 2.35983i) q^{31} +(-3.25414 - 5.63634i) q^{32} +(-0.284829 - 0.0925467i) q^{33} +(1.66913 - 2.89102i) q^{34} +1.00000 q^{35} +(3.24803 + 2.35983i) q^{36} -7.88558 q^{37} +(-0.126381 + 0.218898i) q^{38} +(-4.82331 + 4.34293i) q^{39} +(0.604528 + 1.04707i) q^{40} +(-5.02090 - 8.69645i) q^{41} +(2.35177 - 2.11754i) q^{42} +(-3.69693 + 6.40327i) q^{43} +0.231398 q^{44} +(-2.42705 - 1.76336i) q^{45} -14.2565 q^{46} +(2.90063 - 5.02404i) q^{47} +(8.04791 + 2.61492i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.913545 + 1.58231i) q^{50} +(0.657960 + 3.09546i) q^{51} +(2.50739 - 4.34293i) q^{52} -11.7139 q^{53} +(-9.44183 + 0.992377i) q^{54} -0.172909 q^{55} +(0.604528 - 1.04707i) q^{56} +(-0.0498185 - 0.234378i) q^{57} +(-0.894028 - 1.54850i) q^{58} +(0.590068 + 1.02203i) q^{59} +(2.20449 + 0.716282i) q^{60} +(-3.50138 + 6.06457i) q^{61} +4.97864 q^{62} +(-0.313585 + 2.98357i) q^{63} -2.12007 q^{64} +(-1.87362 + 3.24520i) q^{65} +(-0.406642 + 0.366142i) q^{66} +(2.19098 + 3.79489i) q^{67} +(-1.22256 - 2.11754i) q^{68} +(10.0435 - 9.04324i) q^{69} +(0.913545 - 1.58231i) q^{70} +11.2163 q^{71} +(-3.31359 + 1.47530i) q^{72} -1.60792 q^{73} +(-7.20384 + 12.4774i) q^{74} +(-1.64728 - 0.535233i) q^{75} +(0.0925682 + 0.160333i) q^{76} +(0.0864545 + 0.149744i) q^{77} +(2.46553 + 11.5994i) q^{78} +(7.08327 - 12.2686i) q^{79} +4.88558 q^{80} +(6.02218 - 6.68830i) q^{81} -18.3473 q^{82} +(4.63660 - 8.03082i) q^{83} +(-0.481926 - 2.26728i) q^{84} +(0.913545 + 1.58231i) q^{85} +(6.75463 + 11.6994i) q^{86} +(1.61209 + 0.523798i) q^{87} +(-0.104528 + 0.181049i) q^{88} +11.8868 q^{89} +(-5.00739 + 2.22943i) q^{90} +3.74724 q^{91} +(-5.22112 + 9.04324i) q^{92} +(-3.50739 + 3.15807i) q^{93} +(-5.29972 - 9.17938i) q^{94} +(-0.0691705 - 0.119807i) q^{95} +(8.37723 - 7.54289i) q^{96} +(-5.18907 + 8.98774i) q^{97} -1.82709 q^{98} +(0.0542218 - 0.515886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.913545 1.58231i 0.645974 1.11886i −0.338101 0.941110i \(-0.609785\pi\)
0.984076 0.177750i \(-0.0568820\pi\)
\(3\) 0.360114 + 1.69420i 0.207912 + 0.978148i
\(4\) −0.669131 1.15897i −0.334565 0.579484i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 3.00973 + 0.977920i 1.22872 + 0.399234i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 1.20906 0.427466
\(9\) −2.74064 + 1.22021i −0.913545 + 0.406737i
\(10\) 1.82709 0.577777
\(11\) −0.0864545 + 0.149744i −0.0260670 + 0.0451494i −0.878765 0.477255i \(-0.841632\pi\)
0.852698 + 0.522405i \(0.174965\pi\)
\(12\) 1.72256 1.55100i 0.497261 0.447736i
\(13\) 1.87362 + 3.24520i 0.519648 + 0.900058i 0.999739 + 0.0228387i \(0.00727041\pi\)
−0.480091 + 0.877219i \(0.659396\pi\)
\(14\) −0.913545 1.58231i −0.244155 0.422889i
\(15\) −1.28716 + 1.15897i −0.332344 + 0.299244i
\(16\) 2.44279 4.23104i 0.610697 1.05776i
\(17\) 1.82709 0.443135 0.221567 0.975145i \(-0.428883\pi\)
0.221567 + 0.975145i \(0.428883\pi\)
\(18\) −0.572949 + 5.45125i −0.135045 + 1.28487i
\(19\) −0.138341 −0.0317376 −0.0158688 0.999874i \(-0.505051\pi\)
−0.0158688 + 0.999874i \(0.505051\pi\)
\(20\) 0.669131 1.15897i 0.149622 0.259153i
\(21\) 1.64728 + 0.535233i 0.359466 + 0.116797i
\(22\) 0.157960 + 0.273595i 0.0336773 + 0.0583307i
\(23\) −3.90142 6.75746i −0.813502 1.40903i −0.910398 0.413733i \(-0.864225\pi\)
0.0968960 0.995295i \(-0.469109\pi\)
\(24\) 0.435398 + 2.04839i 0.0888752 + 0.418125i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 6.84655 1.34272
\(27\) −3.05422 4.20378i −0.587785 0.809017i
\(28\) −1.33826 −0.252908
\(29\) 0.489318 0.847523i 0.0908641 0.157381i −0.817011 0.576622i \(-0.804370\pi\)
0.907875 + 0.419241i \(0.137704\pi\)
\(30\) 0.657960 + 3.09546i 0.120127 + 0.565151i
\(31\) 1.36245 + 2.35983i 0.244703 + 0.423838i 0.962048 0.272880i \(-0.0879762\pi\)
−0.717345 + 0.696718i \(0.754643\pi\)
\(32\) −3.25414 5.63634i −0.575256 0.996373i
\(33\) −0.284829 0.0925467i −0.0495824 0.0161103i
\(34\) 1.66913 2.89102i 0.286254 0.495806i
\(35\) 1.00000 0.169031
\(36\) 3.24803 + 2.35983i 0.541338 + 0.393305i
\(37\) −7.88558 −1.29638 −0.648191 0.761478i \(-0.724474\pi\)
−0.648191 + 0.761478i \(0.724474\pi\)
\(38\) −0.126381 + 0.218898i −0.0205017 + 0.0355100i
\(39\) −4.82331 + 4.34293i −0.772348 + 0.695425i
\(40\) 0.604528 + 1.04707i 0.0955843 + 0.165557i
\(41\) −5.02090 8.69645i −0.784132 1.35816i −0.929516 0.368782i \(-0.879775\pi\)
0.145384 0.989375i \(-0.453558\pi\)
\(42\) 2.35177 2.11754i 0.362885 0.326744i
\(43\) −3.69693 + 6.40327i −0.563777 + 0.976490i 0.433386 + 0.901209i \(0.357319\pi\)
−0.997162 + 0.0752814i \(0.976014\pi\)
\(44\) 0.231398 0.0348845
\(45\) −2.42705 1.76336i −0.361803 0.262866i
\(46\) −14.2565 −2.10201
\(47\) 2.90063 5.02404i 0.423100 0.732831i −0.573141 0.819457i \(-0.694275\pi\)
0.996241 + 0.0866257i \(0.0276084\pi\)
\(48\) 8.04791 + 2.61492i 1.16162 + 0.377432i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0.913545 + 1.58231i 0.129195 + 0.223772i
\(51\) 0.657960 + 3.09546i 0.0921329 + 0.433451i
\(52\) 2.50739 4.34293i 0.347713 0.602256i
\(53\) −11.7139 −1.60902 −0.804511 0.593938i \(-0.797572\pi\)
−0.804511 + 0.593938i \(0.797572\pi\)
\(54\) −9.44183 + 0.992377i −1.28487 + 0.135045i
\(55\) −0.172909 −0.0233151
\(56\) 0.604528 1.04707i 0.0807835 0.139921i
\(57\) −0.0498185 0.234378i −0.00659862 0.0310441i
\(58\) −0.894028 1.54850i −0.117392 0.203328i
\(59\) 0.590068 + 1.02203i 0.0768203 + 0.133057i 0.901876 0.431994i \(-0.142190\pi\)
−0.825056 + 0.565051i \(0.808857\pi\)
\(60\) 2.20449 + 0.716282i 0.284598 + 0.0924716i
\(61\) −3.50138 + 6.06457i −0.448306 + 0.776488i −0.998276 0.0586959i \(-0.981306\pi\)
0.549970 + 0.835184i \(0.314639\pi\)
\(62\) 4.97864 0.632287
\(63\) −0.313585 + 2.98357i −0.0395080 + 0.375894i
\(64\) −2.12007 −0.265008
\(65\) −1.87362 + 3.24520i −0.232394 + 0.402518i
\(66\) −0.406642 + 0.366142i −0.0500541 + 0.0450690i
\(67\) 2.19098 + 3.79489i 0.267671 + 0.463620i 0.968260 0.249945i \(-0.0804126\pi\)
−0.700589 + 0.713565i \(0.747079\pi\)
\(68\) −1.22256 2.11754i −0.148257 0.256789i
\(69\) 10.0435 9.04324i 1.20910 1.08868i
\(70\) 0.913545 1.58231i 0.109190 0.189122i
\(71\) 11.2163 1.33113 0.665564 0.746341i \(-0.268191\pi\)
0.665564 + 0.746341i \(0.268191\pi\)
\(72\) −3.31359 + 1.47530i −0.390510 + 0.173866i
\(73\) −1.60792 −0.188193 −0.0940964 0.995563i \(-0.529996\pi\)
−0.0940964 + 0.995563i \(0.529996\pi\)
\(74\) −7.20384 + 12.4774i −0.837429 + 1.45047i
\(75\) −1.64728 0.535233i −0.190211 0.0618034i
\(76\) 0.0925682 + 0.160333i 0.0106183 + 0.0183914i
\(77\) 0.0864545 + 0.149744i 0.00985241 + 0.0170649i
\(78\) 2.46553 + 11.5994i 0.279167 + 1.31338i
\(79\) 7.08327 12.2686i 0.796930 1.38032i −0.124677 0.992197i \(-0.539789\pi\)
0.921607 0.388125i \(-0.126877\pi\)
\(80\) 4.88558 0.546224
\(81\) 6.02218 6.68830i 0.669131 0.743145i
\(82\) −18.3473 −2.02612
\(83\) 4.63660 8.03082i 0.508933 0.881497i −0.491014 0.871152i \(-0.663374\pi\)
0.999946 0.0103453i \(-0.00329307\pi\)
\(84\) −0.481926 2.26728i −0.0525824 0.247381i
\(85\) 0.913545 + 1.58231i 0.0990879 + 0.171625i
\(86\) 6.75463 + 11.6994i 0.728370 + 1.26157i
\(87\) 1.61209 + 0.523798i 0.172834 + 0.0561571i
\(88\) −0.104528 + 0.181049i −0.0111428 + 0.0192998i
\(89\) 11.8868 1.25999 0.629997 0.776598i \(-0.283056\pi\)
0.629997 + 0.776598i \(0.283056\pi\)
\(90\) −5.00739 + 2.22943i −0.527825 + 0.235003i
\(91\) 3.74724 0.392817
\(92\) −5.22112 + 9.04324i −0.544339 + 0.942823i
\(93\) −3.50739 + 3.15807i −0.363700 + 0.327477i
\(94\) −5.29972 9.17938i −0.546624 0.946780i
\(95\) −0.0691705 0.119807i −0.00709675 0.0122919i
\(96\) 8.37723 7.54289i 0.854998 0.769843i
\(97\) −5.18907 + 8.98774i −0.526871 + 0.912567i 0.472639 + 0.881256i \(0.343301\pi\)
−0.999510 + 0.0313105i \(0.990032\pi\)
\(98\) −1.82709 −0.184564
\(99\) 0.0542218 0.515886i 0.00544949 0.0518485i
\(100\) 1.33826 0.133826
\(101\) −8.85160 + 15.3314i −0.880767 + 1.52553i −0.0302779 + 0.999542i \(0.509639\pi\)
−0.850489 + 0.525992i \(0.823694\pi\)
\(102\) 5.49904 + 1.78675i 0.544487 + 0.176914i
\(103\) 1.07860 + 1.86818i 0.106277 + 0.184078i 0.914259 0.405130i \(-0.132774\pi\)
−0.807982 + 0.589207i \(0.799440\pi\)
\(104\) 2.26531 + 3.92364i 0.222132 + 0.384744i
\(105\) 0.360114 + 1.69420i 0.0351435 + 0.165337i
\(106\) −10.7011 + 18.5349i −1.03939 + 1.80027i
\(107\) −11.5229 −1.11396 −0.556979 0.830527i \(-0.688039\pi\)
−0.556979 + 0.830527i \(0.688039\pi\)
\(108\) −2.82837 + 6.35262i −0.272160 + 0.611281i
\(109\) 6.89492 0.660414 0.330207 0.943909i \(-0.392882\pi\)
0.330207 + 0.943909i \(0.392882\pi\)
\(110\) −0.157960 + 0.273595i −0.0150609 + 0.0260863i
\(111\) −2.83970 13.3598i −0.269533 1.26805i
\(112\) −2.44279 4.23104i −0.230822 0.399795i
\(113\) −3.34848 5.79973i −0.314998 0.545593i 0.664439 0.747343i \(-0.268671\pi\)
−0.979437 + 0.201750i \(0.935337\pi\)
\(114\) −0.416369 0.135286i −0.0389965 0.0126707i
\(115\) 3.90142 6.75746i 0.363809 0.630136i
\(116\) −1.30967 −0.121600
\(117\) −9.09474 6.60771i −0.840809 0.610883i
\(118\) 2.15622 0.198496
\(119\) 0.913545 1.58231i 0.0837446 0.145050i
\(120\) −1.55626 + 1.40126i −0.142066 + 0.127917i
\(121\) 5.48505 + 9.50039i 0.498641 + 0.863672i
\(122\) 6.39734 + 11.0805i 0.579188 + 1.00318i
\(123\) 12.9254 11.6381i 1.16545 1.04937i
\(124\) 1.82331 3.15807i 0.163738 0.283603i
\(125\) −1.00000 −0.0894427
\(126\) 4.43444 + 3.22181i 0.395052 + 0.287022i
\(127\) −16.8604 −1.49611 −0.748057 0.663634i \(-0.769013\pi\)
−0.748057 + 0.663634i \(0.769013\pi\)
\(128\) 4.57151 7.91808i 0.404068 0.699866i
\(129\) −12.1797 3.95744i −1.07237 0.348433i
\(130\) 3.42327 + 5.92928i 0.300241 + 0.520032i
\(131\) 6.33458 + 10.9718i 0.553455 + 0.958613i 0.998022 + 0.0628668i \(0.0200243\pi\)
−0.444567 + 0.895746i \(0.646642\pi\)
\(132\) 0.0833294 + 0.392034i 0.00725289 + 0.0341222i
\(133\) −0.0691705 + 0.119807i −0.00599785 + 0.0103886i
\(134\) 8.00625 0.691635
\(135\) 2.11347 4.74692i 0.181898 0.408550i
\(136\) 2.20906 0.189425
\(137\) 1.69555 2.93678i 0.144861 0.250906i −0.784460 0.620179i \(-0.787060\pi\)
0.929321 + 0.369273i \(0.120393\pi\)
\(138\) −5.13396 24.1534i −0.437032 2.05607i
\(139\) −4.06773 7.04551i −0.345020 0.597592i 0.640337 0.768094i \(-0.278795\pi\)
−0.985357 + 0.170501i \(0.945461\pi\)
\(140\) −0.669131 1.15897i −0.0565519 0.0979507i
\(141\) 9.55629 + 3.10503i 0.804785 + 0.261490i
\(142\) 10.2466 17.7476i 0.859874 1.48935i
\(143\) −0.647932 −0.0541828
\(144\) −1.53205 + 14.5764i −0.127671 + 1.21470i
\(145\) 0.978636 0.0812713
\(146\) −1.46891 + 2.54422i −0.121568 + 0.210562i
\(147\) 1.28716 1.15897i 0.106164 0.0955901i
\(148\) 5.27648 + 9.13914i 0.433724 + 0.751232i
\(149\) 2.04131 + 3.53565i 0.167230 + 0.289651i 0.937445 0.348133i \(-0.113184\pi\)
−0.770215 + 0.637785i \(0.779851\pi\)
\(150\) −2.35177 + 2.11754i −0.192021 + 0.172896i
\(151\) 7.85489 13.6051i 0.639222 1.10717i −0.346382 0.938094i \(-0.612590\pi\)
0.985604 0.169071i \(-0.0540769\pi\)
\(152\) −0.167262 −0.0135668
\(153\) −5.00739 + 2.22943i −0.404824 + 0.180239i
\(154\) 0.315921 0.0254576
\(155\) −1.36245 + 2.35983i −0.109435 + 0.189546i
\(156\) 8.26074 + 2.68408i 0.661389 + 0.214898i
\(157\) 1.15280 + 1.99671i 0.0920036 + 0.159355i 0.908354 0.418202i \(-0.137340\pi\)
−0.816351 + 0.577557i \(0.804006\pi\)
\(158\) −12.9418 22.4158i −1.02959 1.78331i
\(159\) −4.21832 19.8456i −0.334534 1.57386i
\(160\) 3.25414 5.63634i 0.257263 0.445592i
\(161\) −7.80284 −0.614950
\(162\) −5.08142 15.6390i −0.399234 1.22872i
\(163\) 18.7421 1.46800 0.733998 0.679152i \(-0.237652\pi\)
0.733998 + 0.679152i \(0.237652\pi\)
\(164\) −6.71927 + 11.6381i −0.524687 + 0.908785i
\(165\) −0.0622669 0.292943i −0.00484747 0.0228056i
\(166\) −8.47148 14.6730i −0.657515 1.13885i
\(167\) 2.85634 + 4.94732i 0.221030 + 0.382835i 0.955121 0.296216i \(-0.0957248\pi\)
−0.734091 + 0.679051i \(0.762392\pi\)
\(168\) 1.99165 + 0.647127i 0.153659 + 0.0499270i
\(169\) −0.520897 + 0.902221i −0.0400690 + 0.0694016i
\(170\) 3.33826 0.256033
\(171\) 0.379143 0.168805i 0.0289938 0.0129089i
\(172\) 9.89492 0.754481
\(173\) 8.83149 15.2966i 0.671446 1.16298i −0.306048 0.952016i \(-0.599007\pi\)
0.977494 0.210963i \(-0.0676598\pi\)
\(174\) 2.30152 2.07230i 0.174478 0.157101i
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) 0.422381 + 0.731585i 0.0318381 + 0.0551453i
\(177\) −1.51903 + 1.36774i −0.114177 + 0.102806i
\(178\) 10.8591 18.8085i 0.813924 1.40976i
\(179\) 3.59700 0.268852 0.134426 0.990924i \(-0.457081\pi\)
0.134426 + 0.990924i \(0.457081\pi\)
\(180\) −0.419659 + 3.99279i −0.0312795 + 0.297605i
\(181\) −13.8362 −1.02844 −0.514219 0.857659i \(-0.671918\pi\)
−0.514219 + 0.857659i \(0.671918\pi\)
\(182\) 3.42327 5.92928i 0.253750 0.439508i
\(183\) −11.5355 3.74811i −0.852728 0.277068i
\(184\) −4.71704 8.17015i −0.347745 0.602312i
\(185\) −3.94279 6.82911i −0.289880 0.502086i
\(186\) 1.79287 + 8.43481i 0.131460 + 0.618470i
\(187\) −0.157960 + 0.273595i −0.0115512 + 0.0200073i
\(188\) −7.76360 −0.566219
\(189\) −5.16769 + 0.543146i −0.375894 + 0.0395080i
\(190\) −0.252762 −0.0183373
\(191\) 2.99212 5.18250i 0.216502 0.374993i −0.737234 0.675637i \(-0.763868\pi\)
0.953736 + 0.300645i \(0.0972018\pi\)
\(192\) −0.763465 3.59182i −0.0550984 0.259217i
\(193\) 8.83948 + 15.3104i 0.636279 + 1.10207i 0.986243 + 0.165305i \(0.0528608\pi\)
−0.349963 + 0.936763i \(0.613806\pi\)
\(194\) 9.48091 + 16.4214i 0.680690 + 1.17899i
\(195\) −6.17274 2.00565i −0.442039 0.143627i
\(196\) −0.669131 + 1.15897i −0.0477950 + 0.0827834i
\(197\) −20.1914 −1.43858 −0.719290 0.694710i \(-0.755533\pi\)
−0.719290 + 0.694710i \(0.755533\pi\)
\(198\) −0.766755 0.557080i −0.0544909 0.0395900i
\(199\) 18.0867 1.28214 0.641068 0.767484i \(-0.278492\pi\)
0.641068 + 0.767484i \(0.278492\pi\)
\(200\) −0.604528 + 1.04707i −0.0427466 + 0.0740393i
\(201\) −5.64031 + 5.07856i −0.397837 + 0.358214i
\(202\) 16.1727 + 28.0119i 1.13791 + 1.97091i
\(203\) −0.489318 0.847523i −0.0343434 0.0594845i
\(204\) 3.14728 2.83382i 0.220354 0.198407i
\(205\) 5.02090 8.69645i 0.350675 0.607386i
\(206\) 3.94139 0.274609
\(207\) 18.9379 + 13.7592i 1.31627 + 0.956329i
\(208\) 18.3074 1.26939
\(209\) 0.0119602 0.0207157i 0.000827305 0.00143293i
\(210\) 3.00973 + 0.977920i 0.207691 + 0.0674829i
\(211\) 11.9382 + 20.6775i 0.821857 + 1.42350i 0.904298 + 0.426902i \(0.140395\pi\)
−0.0824414 + 0.996596i \(0.526272\pi\)
\(212\) 7.83810 + 13.5760i 0.538323 + 0.932402i
\(213\) 4.03914 + 19.0026i 0.276757 + 1.30204i
\(214\) −10.5267 + 18.2327i −0.719588 + 1.24636i
\(215\) −7.39386 −0.504257
\(216\) −3.69273 5.08260i −0.251258 0.345827i
\(217\) 2.72490 0.184978
\(218\) 6.29882 10.9099i 0.426610 0.738910i
\(219\) −0.579034 2.72414i −0.0391275 0.184080i
\(220\) 0.115699 + 0.200396i 0.00780041 + 0.0135107i
\(221\) 3.42327 + 5.92928i 0.230274 + 0.398847i
\(222\) −23.7334 7.71146i −1.59288 0.517559i
\(223\) −3.81407 + 6.60617i −0.255409 + 0.442382i −0.965007 0.262226i \(-0.915544\pi\)
0.709597 + 0.704607i \(0.248877\pi\)
\(224\) −6.50828 −0.434853
\(225\) 0.313585 2.98357i 0.0209057 0.198904i
\(226\) −12.2359 −0.813923
\(227\) −8.09650 + 14.0236i −0.537384 + 0.930776i 0.461660 + 0.887057i \(0.347254\pi\)
−0.999044 + 0.0437192i \(0.986079\pi\)
\(228\) −0.238301 + 0.214567i −0.0157819 + 0.0142101i
\(229\) 12.5200 + 21.6854i 0.827348 + 1.43301i 0.900112 + 0.435659i \(0.143485\pi\)
−0.0727638 + 0.997349i \(0.523182\pi\)
\(230\) −7.12825 12.3465i −0.470023 0.814103i
\(231\) −0.222562 + 0.200396i −0.0146435 + 0.0131851i
\(232\) 0.591613 1.02470i 0.0388413 0.0672751i
\(233\) −10.2963 −0.674536 −0.337268 0.941409i \(-0.609503\pi\)
−0.337268 + 0.941409i \(0.609503\pi\)
\(234\) −18.7639 + 8.35422i −1.22663 + 0.546133i
\(235\) 5.80126 0.378433
\(236\) 0.789665 1.36774i 0.0514028 0.0890323i
\(237\) 23.3362 + 7.58240i 1.51585 + 0.492530i
\(238\) −1.66913 2.89102i −0.108194 0.187397i
\(239\) −9.95235 17.2380i −0.643764 1.11503i −0.984585 0.174904i \(-0.944038\pi\)
0.340821 0.940128i \(-0.389295\pi\)
\(240\) 1.75936 + 8.27716i 0.113566 + 0.534288i
\(241\) −5.19868 + 9.00437i −0.334876 + 0.580023i −0.983461 0.181120i \(-0.942028\pi\)
0.648585 + 0.761142i \(0.275361\pi\)
\(242\) 20.0434 1.28844
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 9.37152 0.599950
\(245\) 0.500000 0.866025i 0.0319438 0.0553283i
\(246\) −6.60710 31.0840i −0.421253 1.98184i
\(247\) −0.259198 0.448945i −0.0164924 0.0285657i
\(248\) 1.64728 + 2.85317i 0.104602 + 0.181176i
\(249\) 15.2755 + 4.96332i 0.968047 + 0.314538i
\(250\) −0.913545 + 1.58231i −0.0577777 + 0.100074i
\(251\) −24.0059 −1.51524 −0.757620 0.652696i \(-0.773638\pi\)
−0.757620 + 0.652696i \(0.773638\pi\)
\(252\) 3.66769 1.63296i 0.231043 0.102867i
\(253\) 1.34918 0.0848223
\(254\) −15.4027 + 26.6783i −0.966451 + 1.67394i
\(255\) −2.35177 + 2.11754i −0.147273 + 0.132606i
\(256\) −10.4726 18.1391i −0.654539 1.13369i
\(257\) 6.03395 + 10.4511i 0.376387 + 0.651922i 0.990534 0.137270i \(-0.0438328\pi\)
−0.614146 + 0.789192i \(0.710500\pi\)
\(258\) −17.3886 + 15.6568i −1.08257 + 0.974750i
\(259\) −3.94279 + 6.82911i −0.244993 + 0.424340i
\(260\) 5.01478 0.311004
\(261\) −0.306886 + 2.91982i −0.0189958 + 0.180733i
\(262\) 23.1477 1.43007
\(263\) −1.93191 + 3.34616i −0.119127 + 0.206333i −0.919422 0.393273i \(-0.871343\pi\)
0.800295 + 0.599606i \(0.204676\pi\)
\(264\) −0.344375 0.111894i −0.0211948 0.00688661i
\(265\) −5.85693 10.1445i −0.359788 0.623171i
\(266\) 0.126381 + 0.218898i 0.00774891 + 0.0134215i
\(267\) 4.28058 + 20.1386i 0.261967 + 1.23246i
\(268\) 2.93211 5.07856i 0.179107 0.310222i
\(269\) 8.48725 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(270\) −5.58034 7.68068i −0.339609 0.467431i
\(271\) 11.8287 0.718541 0.359270 0.933234i \(-0.383026\pi\)
0.359270 + 0.933234i \(0.383026\pi\)
\(272\) 4.46320 7.73049i 0.270621 0.468730i
\(273\) 1.34943 + 6.34858i 0.0816713 + 0.384233i
\(274\) −3.09793 5.36577i −0.187153 0.324158i
\(275\) −0.0864545 0.149744i −0.00521341 0.00902988i
\(276\) −17.2013 5.58903i −1.03539 0.336420i
\(277\) 13.6581 23.6565i 0.820636 1.42138i −0.0845742 0.996417i \(-0.526953\pi\)
0.905210 0.424965i \(-0.139714\pi\)
\(278\) −14.8642 −0.891496
\(279\) −6.61347 4.80496i −0.395938 0.287666i
\(280\) 1.20906 0.0722550
\(281\) −7.94358 + 13.7587i −0.473874 + 0.820774i −0.999553 0.0299091i \(-0.990478\pi\)
0.525678 + 0.850683i \(0.323812\pi\)
\(282\) 13.6432 12.2844i 0.812441 0.731526i
\(283\) −8.23065 14.2559i −0.489261 0.847425i 0.510663 0.859781i \(-0.329400\pi\)
−0.999924 + 0.0123561i \(0.996067\pi\)
\(284\) −7.50516 12.9993i −0.445349 0.771367i
\(285\) 0.178068 0.160333i 0.0105478 0.00949730i
\(286\) −0.591915 + 1.02523i −0.0350007 + 0.0606229i
\(287\) −10.0418 −0.592748
\(288\) 15.7959 + 11.4764i 0.930784 + 0.676255i
\(289\) −13.6617 −0.803632
\(290\) 0.894028 1.54850i 0.0524991 0.0909312i
\(291\) −17.0957 5.55473i −1.00217 0.325624i
\(292\) 1.07591 + 1.86353i 0.0629628 + 0.109055i
\(293\) 11.9116 + 20.6315i 0.695884 + 1.20531i 0.969882 + 0.243576i \(0.0783205\pi\)
−0.273998 + 0.961730i \(0.588346\pi\)
\(294\) −0.657960 3.09546i −0.0383730 0.180531i
\(295\) −0.590068 + 1.02203i −0.0343551 + 0.0595047i
\(296\) −9.53411 −0.554159
\(297\) 0.893540 0.0939148i 0.0518485 0.00544949i
\(298\) 7.45931 0.432106
\(299\) 14.6196 25.3218i 0.845470 1.46440i
\(300\) 0.481926 + 2.26728i 0.0278240 + 0.130902i
\(301\) 3.69693 + 6.40327i 0.213088 + 0.369079i
\(302\) −14.3516 24.8577i −0.825842 1.43040i
\(303\) −29.1621 9.47534i −1.67532 0.544344i
\(304\) −0.337938 + 0.585326i −0.0193821 + 0.0335708i
\(305\) −7.00276 −0.400977
\(306\) −1.04683 + 9.95992i −0.0598433 + 0.569371i
\(307\) −23.7097 −1.35318 −0.676591 0.736359i \(-0.736543\pi\)
−0.676591 + 0.736359i \(0.736543\pi\)
\(308\) 0.115699 0.200396i 0.00659255 0.0114186i
\(309\) −2.77666 + 2.50012i −0.157959 + 0.142227i
\(310\) 2.48932 + 4.31163i 0.141384 + 0.244884i
\(311\) 7.30983 + 12.6610i 0.414502 + 0.717939i 0.995376 0.0960546i \(-0.0306223\pi\)
−0.580874 + 0.813994i \(0.697289\pi\)
\(312\) −5.83166 + 5.25085i −0.330153 + 0.297271i
\(313\) −5.34090 + 9.25071i −0.301885 + 0.522881i −0.976563 0.215232i \(-0.930949\pi\)
0.674678 + 0.738113i \(0.264283\pi\)
\(314\) 4.21255 0.237728
\(315\) −2.74064 + 1.22021i −0.154417 + 0.0687510i
\(316\) −18.9585 −1.06650
\(317\) 10.9564 18.9771i 0.615375 1.06586i −0.374944 0.927047i \(-0.622338\pi\)
0.990319 0.138813i \(-0.0443285\pi\)
\(318\) −35.2555 11.4552i −1.97703 0.642376i
\(319\) 0.0846075 + 0.146545i 0.00473711 + 0.00820492i
\(320\) −1.06003 1.83603i −0.0592577 0.102637i
\(321\) −4.14954 19.5221i −0.231605 1.08961i
\(322\) −7.12825 + 12.3465i −0.397242 + 0.688043i
\(323\) −0.252762 −0.0140640
\(324\) −11.7812 2.50416i −0.654508 0.139120i
\(325\) −3.74724 −0.207859
\(326\) 17.1218 29.6558i 0.948287 1.64248i
\(327\) 2.48295 + 11.6814i 0.137308 + 0.645982i
\(328\) −6.07055 10.5145i −0.335190 0.580566i
\(329\) −2.90063 5.02404i −0.159917 0.276984i
\(330\) −0.520409 0.169091i −0.0286476 0.00930816i
\(331\) 11.2591 19.5014i 0.618858 1.07189i −0.370836 0.928698i \(-0.620929\pi\)
0.989694 0.143195i \(-0.0457377\pi\)
\(332\) −12.4100 −0.681085
\(333\) 21.6115 9.62206i 1.18430 0.527286i
\(334\) 10.4376 0.571118
\(335\) −2.19098 + 3.79489i −0.119706 + 0.207337i
\(336\) 6.28854 5.66223i 0.343068 0.308900i
\(337\) 3.70857 + 6.42343i 0.202019 + 0.349906i 0.949179 0.314738i \(-0.101917\pi\)
−0.747160 + 0.664644i \(0.768583\pi\)
\(338\) 0.951727 + 1.64844i 0.0517671 + 0.0896633i
\(339\) 8.62008 7.76156i 0.468179 0.421550i
\(340\) 1.22256 2.11754i 0.0663028 0.114840i
\(341\) −0.471160 −0.0255147
\(342\) 0.0792624 0.754131i 0.00428602 0.0407787i
\(343\) −1.00000 −0.0539949
\(344\) −4.46980 + 7.74192i −0.240996 + 0.417416i
\(345\) 12.8534 + 4.17634i 0.692006 + 0.224847i
\(346\) −16.1359 27.9483i −0.867474 1.50251i
\(347\) 12.0354 + 20.8459i 0.646094 + 1.11907i 0.984048 + 0.177905i \(0.0569319\pi\)
−0.337954 + 0.941163i \(0.609735\pi\)
\(348\) −0.471630 2.21885i −0.0252820 0.118943i
\(349\) −7.74234 + 13.4101i −0.414438 + 0.717828i −0.995369 0.0961250i \(-0.969355\pi\)
0.580931 + 0.813953i \(0.302688\pi\)
\(350\) 1.82709 0.0976621
\(351\) 7.91966 17.7878i 0.422720 0.949445i
\(352\) 1.12534 0.0599809
\(353\) −10.7716 + 18.6569i −0.573312 + 0.993006i 0.422910 + 0.906172i \(0.361009\pi\)
−0.996223 + 0.0868347i \(0.972325\pi\)
\(354\) 0.776482 + 3.65306i 0.0412696 + 0.194158i
\(355\) 5.60814 + 9.71359i 0.297649 + 0.515544i
\(356\) −7.95379 13.7764i −0.421550 0.730147i
\(357\) 3.00973 + 0.977920i 0.159292 + 0.0517570i
\(358\) 3.28602 5.69156i 0.173672 0.300808i
\(359\) −18.2075 −0.960954 −0.480477 0.877007i \(-0.659536\pi\)
−0.480477 + 0.877007i \(0.659536\pi\)
\(360\) −2.93444 2.13200i −0.154659 0.112366i
\(361\) −18.9809 −0.998993
\(362\) −12.6400 + 21.8932i −0.664345 + 1.15068i
\(363\) −14.1203 + 12.7140i −0.741125 + 0.667312i
\(364\) −2.50739 4.34293i −0.131423 0.227631i
\(365\) −0.803960 1.39250i −0.0420812 0.0728868i
\(366\) −16.4689 + 14.8286i −0.860841 + 0.775105i
\(367\) 12.5959 21.8167i 0.657498 1.13882i −0.323763 0.946138i \(-0.604948\pi\)
0.981261 0.192682i \(-0.0617186\pi\)
\(368\) −38.1214 −1.98722
\(369\) 24.3719 + 17.7073i 1.26875 + 0.921803i
\(370\) −14.4077 −0.749019
\(371\) −5.85693 + 10.1445i −0.304076 + 0.526676i
\(372\) 6.00701 + 1.95179i 0.311449 + 0.101196i
\(373\) 16.3150 + 28.2583i 0.844757 + 1.46316i 0.885832 + 0.464006i \(0.153588\pi\)
−0.0410753 + 0.999156i \(0.513078\pi\)
\(374\) 0.288608 + 0.499883i 0.0149236 + 0.0258484i
\(375\) −0.360114 1.69420i −0.0185962 0.0874882i
\(376\) 3.50703 6.07435i 0.180861 0.313261i
\(377\) 3.66718 0.188869
\(378\) −3.86149 + 8.67306i −0.198614 + 0.446094i
\(379\) −2.59358 −0.133223 −0.0666116 0.997779i \(-0.521219\pi\)
−0.0666116 + 0.997779i \(0.521219\pi\)
\(380\) −0.0925682 + 0.160333i −0.00474865 + 0.00822490i
\(381\) −6.07164 28.5648i −0.311060 1.46342i
\(382\) −5.46688 9.46891i −0.279710 0.484471i
\(383\) 10.8790 + 18.8429i 0.555890 + 0.962829i 0.997834 + 0.0657867i \(0.0209557\pi\)
−0.441944 + 0.897043i \(0.645711\pi\)
\(384\) 15.0611 + 4.89364i 0.768583 + 0.249728i
\(385\) −0.0864545 + 0.149744i −0.00440613 + 0.00763164i
\(386\) 32.3011 1.64408
\(387\) 2.31861 22.0601i 0.117861 1.12138i
\(388\) 13.8887 0.705090
\(389\) 6.03881 10.4595i 0.306180 0.530319i −0.671344 0.741146i \(-0.734283\pi\)
0.977523 + 0.210828i \(0.0676158\pi\)
\(390\) −8.81263 + 7.93493i −0.446245 + 0.401801i
\(391\) −7.12825 12.3465i −0.360491 0.624389i
\(392\) −0.604528 1.04707i −0.0305333 0.0528852i
\(393\) −16.3073 + 14.6832i −0.822595 + 0.740668i
\(394\) −18.4458 + 31.9490i −0.929285 + 1.60957i
\(395\) 14.1665 0.712796
\(396\) −0.634176 + 0.282354i −0.0318686 + 0.0141888i
\(397\) −33.2451 −1.66852 −0.834262 0.551368i \(-0.814106\pi\)
−0.834262 + 0.551368i \(0.814106\pi\)
\(398\) 16.5231 28.6188i 0.828227 1.43453i
\(399\) −0.227886 0.0740447i −0.0114086 0.00370687i
\(400\) 2.44279 + 4.23104i 0.122139 + 0.211552i
\(401\) 8.81576 + 15.2693i 0.440238 + 0.762514i 0.997707 0.0676835i \(-0.0215608\pi\)
−0.557469 + 0.830198i \(0.688227\pi\)
\(402\) 2.88316 + 13.5642i 0.143799 + 0.676521i
\(403\) −5.10542 + 8.84285i −0.254319 + 0.440494i
\(404\) 23.6915 1.17870
\(405\) 8.80333 + 1.87121i 0.437441 + 0.0929809i
\(406\) −1.78806 −0.0887398
\(407\) 0.681744 1.18082i 0.0337928 0.0585309i
\(408\) 0.795511 + 3.74259i 0.0393837 + 0.185286i
\(409\) −6.99886 12.1224i −0.346071 0.599413i 0.639477 0.768811i \(-0.279151\pi\)
−0.985548 + 0.169398i \(0.945818\pi\)
\(410\) −9.17364 15.8892i −0.453054 0.784712i
\(411\) 5.58609 + 1.81503i 0.275541 + 0.0895289i
\(412\) 1.44344 2.50012i 0.0711133 0.123172i
\(413\) 1.18014 0.0580707
\(414\) 39.0719 17.3959i 1.92028 0.854963i
\(415\) 9.27319 0.455203
\(416\) 12.1940 21.1207i 0.597862 1.03553i
\(417\) 10.4717 9.42873i 0.512800 0.461727i
\(418\) −0.0218524 0.0378495i −0.00106884 0.00185128i
\(419\) 9.20103 + 15.9367i 0.449500 + 0.778557i 0.998353 0.0573619i \(-0.0182689\pi\)
−0.548854 + 0.835919i \(0.684936\pi\)
\(420\) 1.72256 1.55100i 0.0840524 0.0756812i
\(421\) −1.38600 + 2.40063i −0.0675497 + 0.117000i −0.897822 0.440358i \(-0.854851\pi\)
0.830272 + 0.557358i \(0.188185\pi\)
\(422\) 43.6242 2.12359
\(423\) −1.81919 + 17.3084i −0.0884521 + 0.841565i
\(424\) −14.1627 −0.687802
\(425\) −0.913545 + 1.58231i −0.0443135 + 0.0767532i
\(426\) 33.7580 + 10.9686i 1.63558 + 0.531432i
\(427\) 3.50138 + 6.06457i 0.169444 + 0.293485i
\(428\) 7.71030 + 13.3546i 0.372691 + 0.645521i
\(429\) −0.233329 1.09773i −0.0112652 0.0529987i
\(430\) −6.75463 + 11.6994i −0.325737 + 0.564193i
\(431\) 6.55882 0.315927 0.157964 0.987445i \(-0.449507\pi\)
0.157964 + 0.987445i \(0.449507\pi\)
\(432\) −25.2471 + 2.65358i −1.21470 + 0.127671i
\(433\) 3.44922 0.165759 0.0828794 0.996560i \(-0.473588\pi\)
0.0828794 + 0.996560i \(0.473588\pi\)
\(434\) 2.48932 4.31163i 0.119491 0.206965i
\(435\) 0.352420 + 1.65801i 0.0168972 + 0.0794953i
\(436\) −4.61360 7.99099i −0.220951 0.382699i
\(437\) 0.539727 + 0.934834i 0.0258186 + 0.0447192i
\(438\) −4.83940 1.57242i −0.231236 0.0751330i
\(439\) 5.45818 9.45384i 0.260505 0.451207i −0.705872 0.708340i \(-0.749444\pi\)
0.966376 + 0.257133i \(0.0827778\pi\)
\(440\) −0.209057 −0.00996640
\(441\) 2.42705 + 1.76336i 0.115574 + 0.0839693i
\(442\) 12.5093 0.595005
\(443\) −6.96293 + 12.0602i −0.330819 + 0.572995i −0.982673 0.185350i \(-0.940658\pi\)
0.651854 + 0.758345i \(0.273992\pi\)
\(444\) −13.5834 + 12.2306i −0.644640 + 0.580436i
\(445\) 5.94338 + 10.2942i 0.281743 + 0.487994i
\(446\) 6.96866 + 12.0701i 0.329976 + 0.571534i
\(447\) −5.25499 + 4.73162i −0.248553 + 0.223798i
\(448\) −1.06003 + 1.83603i −0.0500819 + 0.0867444i
\(449\) 8.71051 0.411075 0.205537 0.978649i \(-0.434106\pi\)
0.205537 + 0.978649i \(0.434106\pi\)
\(450\) −4.43444 3.22181i −0.209042 0.151878i
\(451\) 1.73632 0.0817600
\(452\) −4.48114 + 7.76156i −0.210775 + 0.365073i
\(453\) 25.8784 + 8.40840i 1.21587 + 0.395061i
\(454\) 14.7931 + 25.6223i 0.694272 + 1.20251i
\(455\) 1.87362 + 3.24520i 0.0878366 + 0.152137i
\(456\) −0.0602334 0.283376i −0.00282069 0.0132703i
\(457\) 0.824467 1.42802i 0.0385669 0.0667999i −0.846098 0.533028i \(-0.821054\pi\)
0.884665 + 0.466228i \(0.154387\pi\)
\(458\) 45.7505 2.13778
\(459\) −5.58034 7.68068i −0.260468 0.358503i
\(460\) −10.4422 −0.486872
\(461\) −3.17896 + 5.50612i −0.148059 + 0.256446i −0.930510 0.366266i \(-0.880636\pi\)
0.782451 + 0.622712i \(0.213969\pi\)
\(462\) 0.113767 + 0.535233i 0.00529293 + 0.0249013i
\(463\) −18.5298 32.0946i −0.861153 1.49156i −0.870817 0.491608i \(-0.836409\pi\)
0.00966371 0.999953i \(-0.496924\pi\)
\(464\) −2.39060 4.14064i −0.110981 0.192225i
\(465\) −4.48866 1.45846i −0.208157 0.0676343i
\(466\) −9.40617 + 16.2920i −0.435733 + 0.754711i
\(467\) −11.7091 −0.541834 −0.270917 0.962603i \(-0.587327\pi\)
−0.270917 + 0.962603i \(0.587327\pi\)
\(468\) −1.57256 + 14.9619i −0.0726917 + 0.691616i
\(469\) 4.38197 0.202340
\(470\) 5.29972 9.17938i 0.244458 0.423413i
\(471\) −2.96769 + 2.67212i −0.136744 + 0.123125i
\(472\) 0.713426 + 1.23569i 0.0328381 + 0.0568772i
\(473\) −0.639233 1.10718i −0.0293920 0.0509084i
\(474\) 33.3164 29.9982i 1.53027 1.37786i
\(475\) 0.0691705 0.119807i 0.00317376 0.00549712i
\(476\) −2.44512 −0.112072
\(477\) 32.1034 14.2934i 1.46991 0.654448i
\(478\) −36.3677 −1.66342
\(479\) 12.8295 22.2214i 0.586197 1.01532i −0.408528 0.912746i \(-0.633958\pi\)
0.994725 0.102577i \(-0.0327089\pi\)
\(480\) 10.7210 + 3.48345i 0.489342 + 0.158997i
\(481\) −14.7746 25.5903i −0.673663 1.16682i
\(482\) 9.49845 + 16.4518i 0.432643 + 0.749359i
\(483\) −2.80991 13.2196i −0.127855 0.601512i
\(484\) 7.34043 12.7140i 0.333656 0.577909i
\(485\) −10.3781 −0.471247
\(486\) 24.6657 14.2408i 1.11886 0.645974i
\(487\) −22.1058 −1.00171 −0.500855 0.865531i \(-0.666981\pi\)
−0.500855 + 0.865531i \(0.666981\pi\)
\(488\) −4.23337 + 7.33241i −0.191636 + 0.331923i
\(489\) 6.74929 + 31.7529i 0.305213 + 1.43592i
\(490\) −0.913545 1.58231i −0.0412698 0.0714814i
\(491\) −12.1665 21.0731i −0.549069 0.951015i −0.998339 0.0576186i \(-0.981649\pi\)
0.449270 0.893396i \(-0.351684\pi\)
\(492\) −22.1370 7.19275i −0.998014 0.324274i
\(493\) 0.894028 1.54850i 0.0402650 0.0697410i
\(494\) −0.947158 −0.0426147
\(495\) 0.473881 0.210985i 0.0212994 0.00948309i
\(496\) 13.3127 0.597758
\(497\) 5.60814 9.71359i 0.251560 0.435714i
\(498\) 21.8084 19.6364i 0.977257 0.879926i
\(499\) −11.5859 20.0674i −0.518656 0.898339i −0.999765 0.0216781i \(-0.993099\pi\)
0.481109 0.876661i \(-0.340234\pi\)
\(500\) 0.669131 + 1.15897i 0.0299244 + 0.0518306i
\(501\) −7.35315 + 6.62080i −0.328514 + 0.295796i
\(502\) −21.9305 + 37.9847i −0.978806 + 1.69534i
\(503\) 34.4400 1.53561 0.767803 0.640686i \(-0.221350\pi\)
0.767803 + 0.640686i \(0.221350\pi\)
\(504\) −0.379143 + 3.60730i −0.0168884 + 0.160682i
\(505\) −17.7032 −0.787782
\(506\) 1.23254 2.13482i 0.0547930 0.0949043i
\(507\) −1.71613 0.557603i −0.0762158 0.0247640i
\(508\) 11.2818 + 19.5406i 0.500548 + 0.866974i
\(509\) −20.0258 34.6858i −0.887629 1.53742i −0.842670 0.538430i \(-0.819018\pi\)
−0.0449590 0.998989i \(-0.514316\pi\)
\(510\) 1.20215 + 5.65569i 0.0532322 + 0.250438i
\(511\) −0.803960 + 1.39250i −0.0355651 + 0.0616006i
\(512\) −19.9828 −0.883126
\(513\) 0.422524 + 0.581555i 0.0186549 + 0.0256763i
\(514\) 22.0491 0.972546
\(515\) −1.07860 + 1.86818i −0.0475286 + 0.0823220i
\(516\) 3.56330 + 16.7640i 0.156865 + 0.737993i
\(517\) 0.501545 + 0.868702i 0.0220579 + 0.0382055i
\(518\) 7.20384 + 12.4774i 0.316518 + 0.548226i
\(519\) 29.0959 + 9.45382i 1.27717 + 0.414976i
\(520\) −2.26531 + 3.92364i −0.0993405 + 0.172063i
\(521\) −17.2174 −0.754309 −0.377154 0.926150i \(-0.623097\pi\)
−0.377154 + 0.926150i \(0.623097\pi\)
\(522\) 4.33970 + 3.15298i 0.189944 + 0.138002i
\(523\) 27.1363 1.18659 0.593293 0.804987i \(-0.297828\pi\)
0.593293 + 0.804987i \(0.297828\pi\)
\(524\) 8.47733 14.6832i 0.370334 0.641437i
\(525\) −1.28716 + 1.15897i −0.0561765 + 0.0505815i
\(526\) 3.52977 + 6.11374i 0.153905 + 0.266572i
\(527\) 2.48932 + 4.31163i 0.108436 + 0.187817i
\(528\) −1.08735 + 0.979051i −0.0473207 + 0.0426077i
\(529\) −18.9422 + 32.8088i −0.823572 + 1.42647i
\(530\) −21.4023 −0.929655
\(531\) −2.86425 2.08100i −0.124298 0.0903077i
\(532\) 0.185136 0.00802669
\(533\) 18.8145 32.5877i 0.814946 1.41153i
\(534\) 35.7759 + 11.6243i 1.54817 + 0.503032i
\(535\) −5.76143 9.97909i −0.249088 0.431434i
\(536\) 2.64902 + 4.58824i 0.114420 + 0.198182i
\(537\) 1.29533 + 6.09404i 0.0558976 + 0.262977i
\(538\) 7.75349 13.4294i 0.334277 0.578984i
\(539\) 0.172909 0.00744772
\(540\) −6.91572 + 0.726871i −0.297605 + 0.0312795i
\(541\) 16.6450 0.715624 0.357812 0.933794i \(-0.383523\pi\)
0.357812 + 0.933794i \(0.383523\pi\)
\(542\) 10.8060 18.7166i 0.464159 0.803946i
\(543\) −4.98261 23.4414i −0.213824 1.00596i
\(544\) −5.94561 10.2981i −0.254916 0.441528i
\(545\) 3.44746 + 5.97118i 0.147673 + 0.255777i
\(546\) 11.2782 + 3.66450i 0.482661 + 0.156826i
\(547\) 11.8219 20.4761i 0.505468 0.875495i −0.494512 0.869171i \(-0.664653\pi\)
0.999980 0.00632492i \(-0.00201330\pi\)
\(548\) −4.53818 −0.193861
\(549\) 2.19596 20.8932i 0.0937214 0.891700i
\(550\) −0.315921 −0.0134709
\(551\) −0.0676928 + 0.117247i −0.00288381 + 0.00499490i
\(552\) 12.1432 10.9338i 0.516849 0.465373i
\(553\) −7.08327 12.2686i −0.301211 0.521713i
\(554\) −24.9546 43.2226i −1.06022 1.83635i
\(555\) 10.1500 9.13914i 0.430845 0.387935i
\(556\) −5.44368 + 9.42873i −0.230864 + 0.399867i
\(557\) 37.1981 1.57613 0.788067 0.615590i \(-0.211082\pi\)
0.788067 + 0.615590i \(0.211082\pi\)
\(558\) −13.6446 + 6.07498i −0.577623 + 0.257174i
\(559\) −27.7066 −1.17186
\(560\) 2.44279 4.23104i 0.103227 0.178794i
\(561\) −0.520409 0.169091i −0.0219717 0.00713904i
\(562\) 14.5136 + 25.1384i 0.612221 + 1.06040i
\(563\) 12.8803 + 22.3093i 0.542840 + 0.940226i 0.998739 + 0.0501948i \(0.0159842\pi\)
−0.455900 + 0.890031i \(0.650682\pi\)
\(564\) −2.79578 13.1531i −0.117724 0.553846i
\(565\) 3.34848 5.79973i 0.140871 0.243997i
\(566\) −30.0763 −1.26420
\(567\) −2.78115 8.55951i −0.116797 0.359466i
\(568\) 13.5611 0.569012
\(569\) −2.32571 + 4.02825i −0.0974989 + 0.168873i −0.910649 0.413181i \(-0.864418\pi\)
0.813150 + 0.582054i \(0.197751\pi\)
\(570\) −0.0910229 0.428229i −0.00381253 0.0179365i
\(571\) −13.9779 24.2105i −0.584958 1.01318i −0.994881 0.101056i \(-0.967778\pi\)
0.409923 0.912120i \(-0.365556\pi\)
\(572\) 0.433551 + 0.750932i 0.0181277 + 0.0313980i
\(573\) 9.85771 + 3.20296i 0.411812 + 0.133806i
\(574\) −9.17364 + 15.8892i −0.382900 + 0.663203i
\(575\) 7.80284 0.325401
\(576\) 5.81033 2.58693i 0.242097 0.107789i
\(577\) −5.63651 −0.234651 −0.117326 0.993094i \(-0.537432\pi\)
−0.117326 + 0.993094i \(0.537432\pi\)
\(578\) −12.4806 + 21.6171i −0.519125 + 0.899151i
\(579\) −22.7557 + 20.4893i −0.945696 + 0.851508i
\(580\) −0.654835 1.13421i −0.0271906 0.0470954i
\(581\) −4.63660 8.03082i −0.192358 0.333175i
\(582\) −24.4070 + 21.9761i −1.01170 + 0.910940i
\(583\) 1.01272 1.75407i 0.0419424 0.0726464i
\(584\) −1.94407 −0.0804461
\(585\) 1.17508 11.1801i 0.0485835 0.462242i
\(586\) 43.5272 1.79809
\(587\) −14.8898 + 25.7899i −0.614569 + 1.06446i 0.375892 + 0.926664i \(0.377337\pi\)
−0.990460 + 0.137800i \(0.955997\pi\)
\(588\) −2.20449 0.716282i −0.0909116 0.0295390i
\(589\) −0.188483 0.326462i −0.00776629 0.0134516i
\(590\) 1.07811 + 1.86734i 0.0443850 + 0.0768771i
\(591\) −7.27121 34.2083i −0.299098 1.40714i
\(592\) −19.2628 + 33.3642i −0.791697 + 1.37126i
\(593\) −46.0749 −1.89207 −0.946035 0.324064i \(-0.894951\pi\)
−0.946035 + 0.324064i \(0.894951\pi\)
\(594\) 0.667687 1.49965i 0.0273955 0.0615314i
\(595\) 1.82709 0.0749034
\(596\) 2.73180 4.73162i 0.111899 0.193815i
\(597\) 6.51328 + 30.6426i 0.266571 + 1.25412i
\(598\) −26.7112 46.2652i −1.09230 1.89193i
\(599\) −6.41929 11.1185i −0.262285 0.454291i 0.704564 0.709641i \(-0.251143\pi\)
−0.966849 + 0.255349i \(0.917809\pi\)
\(600\) −1.99165 0.647127i −0.0813089 0.0264189i
\(601\) 0.326789 0.566015i 0.0133300 0.0230883i −0.859283 0.511500i \(-0.829090\pi\)
0.872613 + 0.488411i \(0.162423\pi\)
\(602\) 13.5093 0.550596
\(603\) −10.6353 7.72696i −0.433101 0.314666i
\(604\) −21.0238 −0.855446
\(605\) −5.48505 + 9.50039i −0.222999 + 0.386246i
\(606\) −41.6338 + 37.4872i −1.69126 + 1.52282i
\(607\) −16.0765 27.8453i −0.652524 1.13021i −0.982508 0.186219i \(-0.940377\pi\)
0.329984 0.943987i \(-0.392957\pi\)
\(608\) 0.450181 + 0.779737i 0.0182573 + 0.0316225i
\(609\) 1.25967 1.13421i 0.0510442 0.0459604i
\(610\) −6.39734 + 11.0805i −0.259021 + 0.448637i
\(611\) 21.7387 0.879454
\(612\) 5.93444 + 4.31163i 0.239886 + 0.174287i
\(613\) 7.74782 0.312931 0.156466 0.987683i \(-0.449990\pi\)
0.156466 + 0.987683i \(0.449990\pi\)
\(614\) −21.6599 + 37.5160i −0.874120 + 1.51402i
\(615\) 16.5416 + 5.37470i 0.667023 + 0.216729i
\(616\) 0.104528 + 0.181049i 0.00421157 + 0.00729466i
\(617\) −15.3193 26.5338i −0.616732 1.06821i −0.990078 0.140519i \(-0.955123\pi\)
0.373346 0.927692i \(-0.378210\pi\)
\(618\) 1.41935 + 6.67750i 0.0570945 + 0.268608i
\(619\) −15.9913 + 27.6977i −0.642745 + 1.11327i 0.342073 + 0.939673i \(0.388871\pi\)
−0.984817 + 0.173593i \(0.944462\pi\)
\(620\) 3.64662 0.146452
\(621\) −16.4910 + 37.0395i −0.661762 + 1.48634i
\(622\) 26.7114 1.07103
\(623\) 5.94338 10.2942i 0.238116 0.412430i
\(624\) 6.59275 + 31.0165i 0.263921 + 1.24165i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 9.75831 + 16.9019i 0.390020 + 0.675535i
\(627\) 0.0394036 + 0.0128030i 0.00157363 + 0.000511303i
\(628\) 1.54275 2.67212i 0.0615624 0.106629i
\(629\) −14.4077 −0.574471
\(630\) −0.572949 + 5.45125i −0.0228268 + 0.217183i
\(631\) 8.65557 0.344573 0.172286 0.985047i \(-0.444885\pi\)
0.172286 + 0.985047i \(0.444885\pi\)
\(632\) 8.56407 14.8334i 0.340661 0.590041i
\(633\) −30.7327 + 27.6719i −1.22152 + 1.09986i
\(634\) −20.0184 34.6729i −0.795032 1.37704i
\(635\) −8.43018 14.6015i −0.334541 0.579443i
\(636\) −20.1778 + 18.1682i −0.800103 + 0.720416i
\(637\) 1.87362 3.24520i 0.0742355 0.128580i
\(638\) 0.309171 0.0122402
\(639\) −30.7398 + 13.6862i −1.21605 + 0.541419i
\(640\) 9.14301 0.361409
\(641\) 2.06538 3.57734i 0.0815776 0.141296i −0.822350 0.568982i \(-0.807338\pi\)
0.903928 + 0.427685i \(0.140671\pi\)
\(642\) −34.6807 11.2684i −1.36874 0.444730i
\(643\) −7.21704 12.5003i −0.284612 0.492963i 0.687903 0.725803i \(-0.258532\pi\)
−0.972515 + 0.232840i \(0.925198\pi\)
\(644\) 5.22112 + 9.04324i 0.205741 + 0.356354i
\(645\) −2.66263 12.5267i −0.104841 0.493238i
\(646\) −0.230909 + 0.399947i −0.00908501 + 0.0157357i
\(647\) 28.1790 1.10783 0.553916 0.832573i \(-0.313133\pi\)
0.553916 + 0.832573i \(0.313133\pi\)
\(648\) 7.28115 8.08654i 0.286031 0.317669i
\(649\) −0.204056 −0.00800991
\(650\) −3.42327 + 5.92928i −0.134272 + 0.232566i
\(651\) 0.981273 + 4.61653i 0.0384591 + 0.180936i
\(652\) −12.5409 21.7215i −0.491140 0.850680i
\(653\) 2.96698 + 5.13896i 0.116107 + 0.201103i 0.918222 0.396067i \(-0.129625\pi\)
−0.802115 + 0.597170i \(0.796292\pi\)
\(654\) 20.7518 + 6.74268i 0.811461 + 0.263660i
\(655\) −6.33458 + 10.9718i −0.247513 + 0.428705i
\(656\) −49.0600 −1.91547
\(657\) 4.40673 1.96200i 0.171923 0.0765449i
\(658\) −10.5994 −0.413209
\(659\) −19.7763 + 34.2536i −0.770376 + 1.33433i 0.166981 + 0.985960i \(0.446598\pi\)
−0.937357 + 0.348370i \(0.886735\pi\)
\(660\) −0.297847 + 0.268182i −0.0115937 + 0.0104390i
\(661\) 20.8000 + 36.0266i 0.809025 + 1.40127i 0.913540 + 0.406749i \(0.133338\pi\)
−0.104514 + 0.994523i \(0.533329\pi\)
\(662\) −20.5715 35.6308i −0.799533 1.38483i
\(663\) −8.81263 + 7.93493i −0.342254 + 0.308167i
\(664\) 5.60591 9.70972i 0.217551 0.376810i
\(665\) −0.138341 −0.00536464
\(666\) 4.51803 42.9862i 0.175070 1.66568i
\(667\) −7.63614 −0.295672
\(668\) 3.82252 6.62080i 0.147898 0.256167i
\(669\) −12.5657 4.08284i −0.485817 0.157852i
\(670\) 4.00313 + 6.93362i 0.154654 + 0.267869i
\(671\) −0.605420 1.04862i −0.0233720 0.0404815i
\(672\) −2.34372 11.0263i −0.0904110 0.425350i
\(673\) 16.6716 28.8760i 0.642643 1.11309i −0.342198 0.939628i \(-0.611171\pi\)
0.984841 0.173462i \(-0.0554953\pi\)
\(674\) 13.5518 0.521995
\(675\) 5.16769 0.543146i 0.198904 0.0209057i
\(676\) 1.39419 0.0536228
\(677\) 9.09786 15.7580i 0.349659 0.605628i −0.636530 0.771252i \(-0.719631\pi\)
0.986189 + 0.165625i \(0.0529640\pi\)
\(678\) −4.40633 20.7301i −0.169224 0.796137i
\(679\) 5.18907 + 8.98774i 0.199138 + 0.344918i
\(680\) 1.10453 + 1.91310i 0.0423567 + 0.0733640i
\(681\) −26.6744 8.66704i −1.02216 0.332122i
\(682\) −0.430426 + 0.745519i −0.0164819 + 0.0285474i
\(683\) −14.0903 −0.539150 −0.269575 0.962979i \(-0.586883\pi\)
−0.269575 + 0.962979i \(0.586883\pi\)
\(684\) −0.449336 0.326462i −0.0171808 0.0124826i
\(685\) 3.39110 0.129567
\(686\) −0.913545 + 1.58231i −0.0348793 + 0.0604128i
\(687\) −32.2307 + 29.0207i −1.22968 + 1.10721i
\(688\) 18.0617 + 31.2837i 0.688594 + 1.19268i
\(689\) −21.9473 38.0138i −0.836125 1.44821i
\(690\) 18.3505 16.5228i 0.698590 0.629013i
\(691\) 16.1752 28.0162i 0.615333 1.06579i −0.374993 0.927027i \(-0.622355\pi\)
0.990326 0.138760i \(-0.0443116\pi\)
\(692\) −23.6377 −0.898570
\(693\) −0.419659 0.304900i −0.0159415 0.0115822i
\(694\) 43.9795 1.66944
\(695\) 4.06773 7.04551i 0.154298 0.267251i
\(696\) 1.94910 + 0.633302i 0.0738806 + 0.0240052i
\(697\) −9.17364 15.8892i −0.347476 0.601846i
\(698\) 14.1460 + 24.5015i 0.535432 + 0.927396i
\(699\) −3.70785 17.4441i −0.140244 0.659795i
\(700\) 0.669131 1.15897i 0.0252908 0.0438049i
\(701\) 26.0054 0.982210 0.491105 0.871100i \(-0.336593\pi\)
0.491105 + 0.871100i \(0.336593\pi\)
\(702\) −20.9109 28.7813i −0.789230 1.08628i
\(703\) 1.09090 0.0411441
\(704\) 0.183289 0.317467i 0.00690798 0.0119650i
\(705\) 2.08911 + 9.82850i 0.0786805 + 0.370163i
\(706\) 19.6806 + 34.0878i 0.740690 + 1.28291i
\(707\) 8.85160 + 15.3314i 0.332899 + 0.576598i
\(708\) 2.60160 + 0.845310i 0.0977740 + 0.0317687i
\(709\) 8.55973 14.8259i 0.321467 0.556798i −0.659324 0.751859i \(-0.729157\pi\)
0.980791 + 0.195061i \(0.0624906\pi\)
\(710\) 20.4932 0.769095
\(711\) −4.44242 + 42.2668i −0.166604 + 1.58513i
\(712\) 14.3718 0.538605
\(713\) 10.6310 18.4134i 0.398133 0.689587i
\(714\) 4.29689 3.86894i 0.160807 0.144791i
\(715\) −0.323966 0.561125i −0.0121156 0.0209849i
\(716\) −2.40686 4.16881i −0.0899487 0.155796i
\(717\) 25.6206 23.0689i 0.956820 0.861525i
\(718\) −16.6334 + 28.8098i −0.620751 + 1.07517i
\(719\) 21.1007 0.786923 0.393461 0.919341i \(-0.371278\pi\)
0.393461 + 0.919341i \(0.371278\pi\)
\(720\) −13.3896 + 5.96143i −0.499001 + 0.222169i
\(721\) 2.15719 0.0803380
\(722\) −17.3399 + 30.0336i −0.645324 + 1.11773i
\(723\) −17.1273 5.56501i −0.636972 0.206965i
\(724\) 9.25824 + 16.0357i 0.344080 + 0.595964i
\(725\) 0.489318 + 0.847523i 0.0181728 + 0.0314762i
\(726\) 7.21789 + 33.9575i 0.267881 + 1.26028i
\(727\) −7.34228 + 12.7172i −0.272310 + 0.471655i −0.969453 0.245277i \(-0.921121\pi\)
0.697143 + 0.716932i \(0.254454\pi\)
\(728\) 4.53062 0.167916
\(729\) −8.34346 + 25.6785i −0.309017 + 0.951057i
\(730\) −2.93782 −0.108734
\(731\) −6.75463 + 11.6994i −0.249829 + 0.432717i
\(732\) 3.37481 + 15.8772i 0.124737 + 0.586840i
\(733\) −21.2290 36.7698i −0.784112 1.35812i −0.929528 0.368752i \(-0.879785\pi\)
0.145416 0.989371i \(-0.453548\pi\)
\(734\) −23.0138 39.8610i −0.849454 1.47130i
\(735\) 1.64728 + 0.535233i 0.0607608 + 0.0197424i
\(736\) −25.3915 + 43.9795i −0.935945 + 1.62110i
\(737\) −0.757682 −0.0279096
\(738\) 50.2832 22.3875i 1.85095 0.824096i
\(739\) 28.5354 1.04969 0.524846 0.851197i \(-0.324123\pi\)
0.524846 + 0.851197i \(0.324123\pi\)
\(740\) −5.27648 + 9.13914i −0.193967 + 0.335961i
\(741\) 0.667262 0.600806i 0.0245125 0.0220711i
\(742\) 10.7011 + 18.5349i 0.392851 + 0.680438i
\(743\) −16.1206 27.9217i −0.591408 1.02435i −0.994043 0.108988i \(-0.965239\pi\)
0.402635 0.915360i \(-0.368094\pi\)
\(744\) −4.24064 + 3.81829i −0.155469 + 0.139985i
\(745\) −2.04131 + 3.53565i −0.0747877 + 0.129536i
\(746\) 59.6179 2.18276
\(747\) −2.90794 + 27.6672i −0.106396 + 1.01229i
\(748\) 0.422784 0.0154585
\(749\) −5.76143 + 9.97909i −0.210518 + 0.364628i
\(750\) −3.00973 0.977920i −0.109900 0.0357086i
\(751\) 13.1046 + 22.6978i 0.478192 + 0.828253i 0.999687 0.0250009i \(-0.00795886\pi\)
−0.521495 + 0.853254i \(0.674626\pi\)
\(752\) −14.1713 24.5453i −0.516773 0.895076i
\(753\) −8.64486 40.6709i −0.315036 1.48213i
\(754\) 3.35014 5.80261i 0.122005 0.211319i
\(755\) 15.7098 0.571738
\(756\) 4.08735 + 5.62575i 0.148655 + 0.204607i
\(757\) 15.1032 0.548937 0.274468 0.961596i \(-0.411498\pi\)
0.274468 + 0.961596i \(0.411498\pi\)
\(758\) −2.36935 + 4.10384i −0.0860588 + 0.149058i
\(759\) 0.485859 + 2.28579i 0.0176356 + 0.0829688i
\(760\) −0.0836311 0.144853i −0.00303362 0.00525438i
\(761\) −4.76604 8.25502i −0.172769 0.299244i 0.766618 0.642103i \(-0.221938\pi\)
−0.939387 + 0.342859i \(0.888605\pi\)
\(762\) −50.7451 16.4881i −1.83830 0.597300i
\(763\) 3.44746 5.97118i 0.124806 0.216171i
\(764\) −8.00848 −0.289737
\(765\) −4.43444 3.22181i −0.160328 0.116485i
\(766\) 39.7538 1.43636
\(767\) −2.21112 + 3.82978i −0.0798391 + 0.138285i
\(768\) 26.9600 24.2749i 0.972835 0.875944i
\(769\) 14.5886 + 25.2682i 0.526079 + 0.911196i 0.999538 + 0.0303802i \(0.00967182\pi\)
−0.473459 + 0.880816i \(0.656995\pi\)
\(770\) 0.157960 + 0.273595i 0.00569249 + 0.00985969i
\(771\) −15.5334 + 13.9863i −0.559421 + 0.503705i
\(772\) 11.8295 20.4893i 0.425754 0.737428i
\(773\) −2.52384 −0.0907762 −0.0453881 0.998969i \(-0.514452\pi\)
−0.0453881 + 0.998969i \(0.514452\pi\)
\(774\) −32.7877 23.8216i −1.17853 0.856251i
\(775\) −2.72490 −0.0978812
\(776\) −6.27388 + 10.8667i −0.225219 + 0.390091i
\(777\) −12.9897 4.22062i −0.466004 0.151414i
\(778\) −11.0334 19.1105i −0.395568 0.685144i
\(779\) 0.694596 + 1.20308i 0.0248865 + 0.0431047i
\(780\) 1.80589 + 8.49605i 0.0646613 + 0.304208i
\(781\) −0.969699 + 1.67957i −0.0346985 + 0.0600996i
\(782\) −26.0479 −0.931472
\(783\) −5.05728 + 0.531542i −0.180733 + 0.0189958i
\(784\) −4.88558 −0.174485
\(785\) −1.15280 + 1.99671i −0.0411453 + 0.0712657i
\(786\) 8.33581 + 39.2169i 0.297329 + 1.39882i
\(787\) −4.55935 7.89702i −0.162523 0.281498i 0.773250 0.634102i \(-0.218630\pi\)
−0.935773 + 0.352603i \(0.885297\pi\)
\(788\) 13.5107 + 23.4012i 0.481299 + 0.833634i
\(789\) −6.36478 2.06804i −0.226592 0.0736243i
\(790\) 12.9418 22.4158i 0.460448 0.797519i
\(791\) −6.69695 −0.238116
\(792\) 0.0655572 0.623735i 0.00232947 0.0221635i
\(793\) −26.2410 −0.931846
\(794\) −30.3709 + 52.6040i −1.07782 + 1.86685i
\(795\) 15.0777 13.5760i 0.534749 0.481490i
\(796\) −12.1024 20.9620i −0.428958 0.742977i
\(797\) −21.3529 36.9843i −0.756358 1.31005i −0.944696 0.327946i \(-0.893644\pi\)
0.188339 0.982104i \(-0.439690\pi\)
\(798\) −0.325346 + 0.292943i −0.0115171 + 0.0103701i
\(799\) 5.29972 9.17938i 0.187490 0.324743i
\(800\) 6.50828 0.230103
\(801\) −32.5773 + 14.5043i −1.15106 + 0.512486i
\(802\) 32.2144 1.13753
\(803\) 0.139012 0.240776i 0.00490563 0.00849680i
\(804\) 9.65999 + 3.13872i 0.340682 + 0.110694i
\(805\) −3.90142 6.75746i −0.137507 0.238169i
\(806\) 9.32807 + 16.1567i 0.328567 + 0.569095i
\(807\) 3.05637 + 14.3791i 0.107589 + 0.506169i
\(808\) −10.7021 + 18.5366i −0.376498 + 0.652114i
\(809\) −4.68059 −0.164561 −0.0822804 0.996609i \(-0.526220\pi\)
−0.0822804 + 0.996609i \(0.526220\pi\)
\(810\) 11.0031 12.2201i 0.386608 0.429372i
\(811\) 33.6854 1.18285 0.591427 0.806359i \(-0.298565\pi\)
0.591427 + 0.806359i \(0.298565\pi\)
\(812\) −0.654835 + 1.13421i −0.0229802 + 0.0398029i
\(813\) 4.25967 + 20.0401i 0.149393 + 0.702839i
\(814\) −1.24561 2.15746i −0.0436586 0.0756188i
\(815\) 9.37106 + 16.2311i 0.328254 + 0.568552i
\(816\) 14.7043 + 4.77770i 0.514752 + 0.167253i
\(817\) 0.511437 0.885836i 0.0178929 0.0309915i
\(818\) −25.5751 −0.894212
\(819\) −10.2698 + 4.57242i −0.358856 + 0.159773i
\(820\) −13.4385 −0.469294
\(821\) 3.95458 6.84954i 0.138016 0.239051i −0.788730 0.614740i \(-0.789261\pi\)
0.926746 + 0.375690i \(0.122594\pi\)
\(822\) 7.97508 7.18080i 0.278163 0.250459i
\(823\) 21.8538 + 37.8519i 0.761775 + 1.31943i 0.941935 + 0.335795i \(0.109005\pi\)
−0.180160 + 0.983637i \(0.557662\pi\)
\(824\) 1.30408 + 2.25874i 0.0454299 + 0.0786869i
\(825\) 0.222562 0.200396i 0.00774863 0.00697690i
\(826\) 1.07811 1.86734i 0.0375122 0.0649730i
\(827\) −23.5601 −0.819265 −0.409633 0.912251i \(-0.634343\pi\)
−0.409633 + 0.912251i \(0.634343\pi\)
\(828\) 3.27453 31.1551i 0.113798 1.08271i
\(829\) −27.9043 −0.969156 −0.484578 0.874748i \(-0.661027\pi\)
−0.484578 + 0.874748i \(0.661027\pi\)
\(830\) 8.47148 14.6730i 0.294049 0.509309i
\(831\) 44.9974 + 14.6205i 1.56094 + 0.507181i
\(832\) −3.97220 6.88005i −0.137711 0.238523i
\(833\) −0.913545 1.58231i −0.0316525 0.0548237i
\(834\) −5.35281 25.1830i −0.185353 0.872015i
\(835\) −2.85634 + 4.94732i −0.0988476 + 0.171209i
\(836\) −0.0320118 −0.00110715
\(837\) 5.75898 12.9349i 0.199059 0.447095i
\(838\) 33.6222 1.16146
\(839\) −2.51039 + 4.34813i −0.0866684 + 0.150114i −0.906101 0.423062i \(-0.860955\pi\)
0.819433 + 0.573176i \(0.194289\pi\)
\(840\) 0.435398 + 2.04839i 0.0150227 + 0.0706760i
\(841\) 14.0211 + 24.2853i 0.483487 + 0.837425i
\(842\) 2.53236 + 4.38617i 0.0872708 + 0.151157i
\(843\) −26.1706 8.50333i −0.901362 0.292870i
\(844\) 15.9764 27.6719i 0.549929 0.952506i
\(845\) −1.04179 −0.0358388
\(846\) 25.7254 + 18.6906i 0.884456 + 0.642595i
\(847\) 10.9701 0.376937
\(848\) −28.6145 + 49.5617i −0.982625 + 1.70196i
\(849\) 21.1884 19.0781i 0.727184 0.654759i
\(850\) 1.66913 + 2.89102i 0.0572507 + 0.0991611i
\(851\) 30.7650 + 53.2865i 1.05461 + 1.82664i
\(852\) 19.3207 17.3965i 0.661918 0.595994i
\(853\) 8.91069 15.4338i 0.305096 0.528442i −0.672186 0.740382i \(-0.734645\pi\)
0.977283 + 0.211940i \(0.0679780\pi\)
\(854\) 12.7947 0.437825
\(855\) 0.335761 + 0.243945i 0.0114828 + 0.00834273i
\(856\) −13.9318 −0.476179
\(857\) −12.9518 + 22.4332i −0.442425 + 0.766303i −0.997869 0.0652514i \(-0.979215\pi\)
0.555444 + 0.831554i \(0.312548\pi\)
\(858\) −1.95010 0.633625i −0.0665752 0.0216316i
\(859\) −9.01087 15.6073i −0.307447 0.532514i 0.670356 0.742039i \(-0.266141\pi\)
−0.977803 + 0.209526i \(0.932808\pi\)
\(860\) 4.94746 + 8.56925i 0.168707 + 0.292209i
\(861\) −3.61619 17.0128i −0.123239 0.579795i
\(862\) 5.99178 10.3781i 0.204081 0.353478i
\(863\) 24.3762 0.829774 0.414887 0.909873i \(-0.363821\pi\)
0.414887 + 0.909873i \(0.363821\pi\)
\(864\) −13.7550 + 30.8943i −0.467956 + 1.05105i
\(865\) 17.6630 0.600560
\(866\) 3.15102 5.45772i 0.107076 0.185461i
\(867\) −4.91978 23.1457i −0.167084 0.786070i
\(868\) −1.82331 3.15807i −0.0618873 0.107192i
\(869\) 1.22476 + 2.12135i 0.0415472 + 0.0719618i
\(870\) 2.94543 + 0.957027i 0.0998593 + 0.0324463i
\(871\) −8.21014 + 14.2204i −0.278190 + 0.481839i
\(872\) 8.33635 0.282304
\(873\) 3.25443 30.9639i 0.110146 1.04797i
\(874\) 1.97226 0.0667127
\(875\) −0.500000 + 0.866025i −0.0169031 + 0.0292770i
\(876\) −2.76974 + 2.49389i −0.0935810 + 0.0842607i
\(877\) 16.4715 + 28.5294i 0.556202 + 0.963370i 0.997809 + 0.0661615i \(0.0210753\pi\)
−0.441607 + 0.897209i \(0.645591\pi\)
\(878\) −9.97259 17.2730i −0.336558 0.582936i
\(879\) −30.6644 + 27.6104i −1.03429 + 0.931274i
\(880\) −0.422381 + 0.731585i −0.0142384 + 0.0246617i
\(881\) −22.2765 −0.750513 −0.375257 0.926921i \(-0.622445\pi\)
−0.375257 + 0.926921i \(0.622445\pi\)
\(882\) 5.00739 2.22943i 0.168608 0.0750690i
\(883\) −5.07478 −0.170780 −0.0853900 0.996348i \(-0.527214\pi\)
−0.0853900 + 0.996348i \(0.527214\pi\)
\(884\) 4.58123 7.93493i 0.154084 0.266881i
\(885\) −1.94401 0.631648i −0.0653472 0.0212326i
\(886\) 12.7219 + 22.0350i 0.427401 + 0.740280i
\(887\) 4.30954 + 7.46434i 0.144700 + 0.250628i 0.929261 0.369424i \(-0.120445\pi\)
−0.784561 + 0.620052i \(0.787112\pi\)
\(888\) −3.43336 16.1527i −0.115216 0.542049i
\(889\) −8.43018 + 14.6015i −0.282739 + 0.489718i
\(890\) 21.7182 0.727995
\(891\) 0.480887 + 1.48002i 0.0161103 + 0.0495824i
\(892\) 10.2085 0.341804
\(893\) −0.401276 + 0.695031i −0.0134282 + 0.0232583i
\(894\) 2.68620 + 12.6376i 0.0898399 + 0.422663i
\(895\) 1.79850 + 3.11509i 0.0601172 + 0.104126i
\(896\) −4.57151 7.91808i −0.152723 0.264524i
\(897\) 48.1649 + 15.6497i 1.60818 + 0.522529i
\(898\) 7.95745 13.7827i 0.265544 0.459935i
\(899\) 2.66668 0.0889388
\(900\) −3.66769 + 1.63296i −0.122256 + 0.0544320i
\(901\) −21.4023 −0.713013
\(902\) 1.58620 2.74739i 0.0528148 0.0914780i
\(903\) −9.51712 + 8.56925i −0.316710 + 0.285167i
\(904\) −4.04850 7.01221i −0.134651 0.233222i
\(905\) −6.91811 11.9825i −0.229966 0.398313i
\(906\) 36.9457 33.2661i 1.22744 1.10519i
\(907\) 24.1539 41.8358i 0.802017 1.38914i −0.116269 0.993218i \(-0.537093\pi\)
0.918286 0.395917i \(-0.129573\pi\)
\(908\) 21.6705 0.719160
\(909\) 5.55147 52.8187i 0.184131 1.75188i
\(910\) 6.84655 0.226961
\(911\) 8.60304 14.9009i 0.285032 0.493689i −0.687585 0.726104i \(-0.741329\pi\)
0.972617 + 0.232415i \(0.0746626\pi\)
\(912\) −1.11336 0.361751i −0.0368669 0.0119788i
\(913\) 0.801710 + 1.38860i 0.0265327 + 0.0459560i
\(914\) −1.50638 2.60912i −0.0498265 0.0863020i
\(915\) −2.52179 11.8641i −0.0833678 0.392215i
\(916\) 16.7551 29.0207i 0.553604 0.958870i
\(917\) 12.6692 0.418373
\(918\) −17.2511 + 1.81316i −0.569371 + 0.0598433i
\(919\) 32.7547 1.08048 0.540240 0.841511i \(-0.318334\pi\)
0.540240 + 0.841511i \(0.318334\pi\)
\(920\) 4.71704 8.17015i 0.155516 0.269362i
\(921\) −8.53817 40.1689i −0.281342 1.32361i
\(922\) 5.80825 + 10.0602i 0.191284 + 0.331314i
\(923\) 21.0150 + 36.3991i 0.691719 + 1.19809i
\(924\) 0.381176 + 0.123852i 0.0125398 + 0.00407442i
\(925\) 3.94279 6.82911i 0.129638 0.224540i
\(926\) −67.7113 −2.22513
\(927\) −5.23561 3.80390i −0.171960 0.124936i
\(928\) −6.36924 −0.209081
\(929\) 19.9714 34.5916i 0.655242 1.13491i −0.326591 0.945166i \(-0.605900\pi\)
0.981833 0.189746i \(-0.0607666\pi\)
\(930\) −6.40832 + 5.77008i −0.210137 + 0.189208i
\(931\) 0.0691705 + 0.119807i 0.00226697 + 0.00392651i
\(932\) 6.88960 + 11.9331i 0.225676 + 0.390883i
\(933\) −18.8179 + 16.9437i −0.616071 + 0.554712i
\(934\) −10.6968 + 18.5275i −0.350011 + 0.606237i
\(935\) −0.315921 −0.0103317
\(936\) −10.9961 7.98910i −0.359417 0.261132i
\(937\) −44.0780 −1.43997 −0.719983 0.693992i \(-0.755850\pi\)
−0.719983 + 0.693992i \(0.755850\pi\)
\(938\) 4.00313 6.93362i 0.130707 0.226391i
\(939\) −17.5959 5.71725i −0.574220 0.186575i
\(940\) −3.88180 6.72348i −0.126610 0.219296i
\(941\) −11.8989 20.6094i −0.387892 0.671848i 0.604274 0.796777i \(-0.293463\pi\)
−0.992166 + 0.124928i \(0.960130\pi\)
\(942\) 1.51700 + 7.13690i 0.0494264 + 0.232533i
\(943\) −39.1773 + 67.8570i −1.27579 + 2.20973i
\(944\) 5.76565 0.187656
\(945\) −3.05422 4.20378i −0.0993538 0.136749i
\(946\) −2.33587 −0.0759458
\(947\) 1.69901 2.94277i 0.0552103 0.0956271i −0.837099 0.547051i \(-0.815750\pi\)
0.892310 + 0.451424i \(0.149084\pi\)
\(948\) −6.82722 32.1196i −0.221738 1.04319i
\(949\) −3.01263 5.21803i −0.0977941 0.169384i
\(950\) −0.126381 0.218898i −0.00410034 0.00710199i
\(951\) 36.0966 + 11.7285i 1.17051 + 0.380322i
\(952\) 1.10453 1.91310i 0.0357980 0.0620039i
\(953\) 43.2045 1.39953 0.699765 0.714373i \(-0.253288\pi\)
0.699765 + 0.714373i \(0.253288\pi\)
\(954\) 6.71144 63.8551i 0.217291 2.06738i
\(955\) 5.98424 0.193645
\(956\) −13.3188 + 23.0689i −0.430762 + 0.746102i
\(957\) −0.217808 + 0.196115i −0.00704072 + 0.00633949i
\(958\) −23.4408 40.6006i −0.757336 1.31175i
\(959\) −1.69555 2.93678i −0.0547522 0.0948336i
\(960\) 2.72888 2.45709i 0.0880741 0.0793023i
\(961\) 11.7875 20.4165i 0.380241 0.658596i
\(962\) −53.9890 −1.74067
\(963\) 31.5800 14.0603i 1.01765 0.453087i
\(964\) 13.9144 0.448152
\(965\) −8.83948 + 15.3104i −0.284553 + 0.492860i
\(966\) −23.4844 7.63055i −0.755599 0.245509i
\(967\) −3.85325 6.67402i −0.123912 0.214622i 0.797395 0.603458i \(-0.206211\pi\)
−0.921307 + 0.388836i \(0.872877\pi\)
\(968\) 6.63174 + 11.4865i 0.213152 + 0.369190i
\(969\) −0.0910229 0.428229i −0.00292408 0.0137567i
\(970\) −9.48091 + 16.4214i −0.304414 + 0.527260i
\(971\) −3.89455 −0.124982 −0.0624911 0.998046i \(-0.519905\pi\)
−0.0624911 + 0.998046i \(0.519905\pi\)
\(972\) 20.8614i 0.669131i
\(973\) −8.13545 −0.260811
\(974\) −20.1947 + 34.9782i −0.647079 + 1.12077i
\(975\) −1.34943 6.34858i −0.0432164 0.203317i
\(976\) 17.1063 + 29.6289i 0.547558 + 0.948399i
\(977\) −3.89947 6.75408i −0.124755 0.216082i 0.796882 0.604135i \(-0.206481\pi\)
−0.921637 + 0.388053i \(0.873148\pi\)
\(978\) 56.4086 + 18.3283i 1.80375 + 0.586074i
\(979\) −1.02766 + 1.77997i −0.0328443 + 0.0568880i
\(980\) −1.33826 −0.0427492
\(981\) −18.8965 + 8.41325i −0.603318 + 0.268614i
\(982\) −44.4588 −1.41874
\(983\) −2.19529 + 3.80236i −0.0700189 + 0.121276i −0.898909 0.438135i \(-0.855639\pi\)
0.828890 + 0.559411i \(0.188973\pi\)
\(984\) 15.6276 14.0712i 0.498190 0.448572i
\(985\) −10.0957 17.4863i −0.321676 0.557160i
\(986\) −1.63347 2.82925i −0.0520203 0.0901018i
\(987\) 7.46718 6.72348i 0.237683 0.214011i
\(988\) −0.346875 + 0.600806i −0.0110356 + 0.0191142i
\(989\) 57.6931 1.83453
\(990\) 0.0990681 0.942570i 0.00314859 0.0299568i
\(991\) 4.07623 0.129486 0.0647428 0.997902i \(-0.479377\pi\)
0.0647428 + 0.997902i \(0.479377\pi\)
\(992\) 8.86720 15.3584i 0.281534 0.487631i
\(993\) 37.0939 + 12.0525i 1.17714 + 0.382475i
\(994\) −10.2466 17.7476i −0.325002 0.562920i
\(995\) 9.04337 + 15.6636i 0.286694 + 0.496569i
\(996\) −4.46899 21.0250i −0.141605 0.666201i
\(997\) 11.8064 20.4492i 0.373911 0.647633i −0.616252 0.787549i \(-0.711350\pi\)
0.990163 + 0.139916i \(0.0446832\pi\)
\(998\) −42.3370 −1.34015
\(999\) 24.0843 + 33.1492i 0.761994 + 1.04879i
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 315.2.i.d.106.4 8
3.2 odd 2 945.2.i.c.316.1 8
9.2 odd 6 2835.2.a.q.1.4 4
9.4 even 3 inner 315.2.i.d.211.4 yes 8
9.5 odd 6 945.2.i.c.631.1 8
9.7 even 3 2835.2.a.l.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.i.d.106.4 8 1.1 even 1 trivial
315.2.i.d.211.4 yes 8 9.4 even 3 inner
945.2.i.c.316.1 8 3.2 odd 2
945.2.i.c.631.1 8 9.5 odd 6
2835.2.a.l.1.1 4 9.7 even 3
2835.2.a.q.1.4 4 9.2 odd 6