Properties

Label 96.3.m.a.19.6
Level $96$
Weight $3$
Character 96.19
Analytic conductor $2.616$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [96,3,Mod(19,96)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(96, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 7, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("96.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.m (of order \(8\), degree \(4\), 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: \(2.61581053786\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.6
Character \(\chi\) \(=\) 96.19
Dual form 96.3.m.a.91.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.19507 - 1.60369i) q^{2} +(1.60021 + 0.662827i) q^{3} +(-1.14363 + 3.83303i) q^{4} +(2.44597 - 1.01315i) q^{5} +(-0.849386 - 3.35835i) q^{6} +(3.89082 + 3.89082i) q^{7} +(7.51370 - 2.74670i) q^{8} +(2.12132 + 2.12132i) q^{9} +O(q^{10})\) \(q+(-1.19507 - 1.60369i) q^{2} +(1.60021 + 0.662827i) q^{3} +(-1.14363 + 3.83303i) q^{4} +(2.44597 - 1.01315i) q^{5} +(-0.849386 - 3.35835i) q^{6} +(3.89082 + 3.89082i) q^{7} +(7.51370 - 2.74670i) q^{8} +(2.12132 + 2.12132i) q^{9} +(-4.54788 - 2.71179i) q^{10} +(10.8967 - 4.51357i) q^{11} +(-4.37068 + 5.37561i) q^{12} +(-1.49885 - 0.620845i) q^{13} +(1.58987 - 10.8895i) q^{14} +4.58561 q^{15} +(-13.3842 - 8.76713i) q^{16} -10.5506i q^{17} +(0.866816 - 5.93706i) q^{18} +(0.916933 - 2.21367i) q^{19} +(1.08617 + 10.5342i) q^{20} +(3.64718 + 8.80506i) q^{21} +(-20.2607 - 12.0809i) q^{22} +(8.67649 - 8.67649i) q^{23} +(13.8441 + 0.584991i) q^{24} +(-12.7214 + 12.7214i) q^{25} +(0.795588 + 3.14564i) q^{26} +(1.98848 + 4.80062i) q^{27} +(-19.3633 + 10.4640i) q^{28} +(-13.5168 + 32.6324i) q^{29} +(-5.48011 - 7.35388i) q^{30} +24.1021i q^{31} +(1.93531 + 31.9414i) q^{32} +20.4287 q^{33} +(-16.9199 + 12.6087i) q^{34} +(13.4588 + 5.57484i) q^{35} +(-10.5571 + 5.70508i) q^{36} +(-56.6116 + 23.4493i) q^{37} +(-4.64583 + 1.17501i) q^{38} +(-1.98696 - 1.98696i) q^{39} +(15.5955 - 14.3309i) q^{40} +(-52.9112 - 52.9112i) q^{41} +(9.76195 - 16.3716i) q^{42} +(65.1237 - 26.9751i) q^{43} +(4.83884 + 46.9293i) q^{44} +(7.33791 + 3.03946i) q^{45} +(-24.2834 - 3.54539i) q^{46} -45.0745 q^{47} +(-15.6064 - 22.9006i) q^{48} -18.7230i q^{49} +(35.6040 + 5.19822i) q^{50} +(6.99325 - 16.8832i) q^{51} +(4.09385 - 5.03513i) q^{52} +(-0.762732 - 1.84140i) q^{53} +(5.32233 - 8.92597i) q^{54} +(22.0801 - 22.0801i) q^{55} +(39.9214 + 18.5475i) q^{56} +(2.93456 - 2.93456i) q^{57} +(68.4857 - 17.3212i) q^{58} +(-19.2287 - 46.4222i) q^{59} +(-5.24423 + 17.5768i) q^{60} +(-12.5097 + 30.2011i) q^{61} +(38.6522 - 28.8036i) q^{62} +16.5074i q^{63} +(48.9113 - 41.2758i) q^{64} -4.29516 q^{65} +(-24.4137 - 32.7613i) q^{66} +(105.419 + 43.6660i) q^{67} +(40.4409 + 12.0660i) q^{68} +(19.6352 - 8.13316i) q^{69} +(-7.14393 - 28.2461i) q^{70} +(-91.7160 - 91.7160i) q^{71} +(21.7656 + 10.1123i) q^{72} +(-67.6747 - 67.6747i) q^{73} +(105.260 + 62.7638i) q^{74} +(-28.7889 + 11.9248i) q^{75} +(7.43644 + 6.04625i) q^{76} +(59.9588 + 24.8357i) q^{77} +(-0.811914 + 5.56102i) q^{78} -74.7323 q^{79} +(-41.6199 - 7.88386i) q^{80} +9.00000i q^{81} +(-21.6206 + 148.086i) q^{82} +(-33.8502 + 81.7215i) q^{83} +(-37.9211 + 3.91000i) q^{84} +(-10.6894 - 25.8065i) q^{85} +(-121.087 - 72.2011i) q^{86} +(-43.2593 + 43.2593i) q^{87} +(69.4773 - 63.8437i) q^{88} +(-9.53321 + 9.53321i) q^{89} +(-3.89495 - 15.4001i) q^{90} +(-3.41617 - 8.24737i) q^{91} +(23.3346 + 43.1799i) q^{92} +(-15.9755 + 38.5683i) q^{93} +(53.8671 + 72.2855i) q^{94} -6.34357i q^{95} +(-18.0748 + 52.3956i) q^{96} +92.4092 q^{97} +(-30.0258 + 22.3752i) q^{98} +(32.6902 + 13.5407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 40 q^{10} + 48 q^{12} + 32 q^{14} - 8 q^{16} - 24 q^{18} - 160 q^{20} - 184 q^{22} + 128 q^{23} - 72 q^{24} - 200 q^{26} - 120 q^{28} + 40 q^{32} + 120 q^{34} - 192 q^{35} + 280 q^{38} + 584 q^{40} - 192 q^{43} + 104 q^{44} + 32 q^{46} - 312 q^{50} - 192 q^{51} - 424 q^{52} + 320 q^{53} - 72 q^{54} - 256 q^{55} - 392 q^{56} - 352 q^{58} - 256 q^{59} - 144 q^{60} + 64 q^{61} - 48 q^{62} + 408 q^{64} + 144 q^{66} + 64 q^{67} + 856 q^{68} - 192 q^{69} + 984 q^{70} + 512 q^{71} + 1056 q^{74} + 384 q^{75} + 296 q^{76} - 448 q^{77} + 360 q^{78} + 512 q^{79} + 328 q^{80} - 760 q^{82} - 448 q^{86} - 1072 q^{88} + 192 q^{91} - 784 q^{92} - 480 q^{94} + 600 q^{96} + 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19507 1.60369i −0.597534 0.801844i
\(3\) 1.60021 + 0.662827i 0.533402 + 0.220942i
\(4\) −1.14363 + 3.83303i −0.285907 + 0.958257i
\(5\) 2.44597 1.01315i 0.489194 0.202631i −0.124431 0.992228i \(-0.539711\pi\)
0.613625 + 0.789597i \(0.289711\pi\)
\(6\) −0.849386 3.35835i −0.141564 0.559726i
\(7\) 3.89082 + 3.89082i 0.555832 + 0.555832i 0.928118 0.372286i \(-0.121426\pi\)
−0.372286 + 0.928118i \(0.621426\pi\)
\(8\) 7.51370 2.74670i 0.939212 0.343338i
\(9\) 2.12132 + 2.12132i 0.235702 + 0.235702i
\(10\) −4.54788 2.71179i −0.454788 0.271179i
\(11\) 10.8967 4.51357i 0.990612 0.410325i 0.172266 0.985051i \(-0.444891\pi\)
0.818346 + 0.574726i \(0.194891\pi\)
\(12\) −4.37068 + 5.37561i −0.364223 + 0.447967i
\(13\) −1.49885 0.620845i −0.115296 0.0477573i 0.324290 0.945958i \(-0.394875\pi\)
−0.439586 + 0.898201i \(0.644875\pi\)
\(14\) 1.58987 10.8895i 0.113562 0.777819i
\(15\) 4.58561 0.305707
\(16\) −13.3842 8.76713i −0.836514 0.547946i
\(17\) 10.5506i 0.620625i −0.950635 0.310313i \(-0.899566\pi\)
0.950635 0.310313i \(-0.100434\pi\)
\(18\) 0.866816 5.93706i 0.0481564 0.329836i
\(19\) 0.916933 2.21367i 0.0482596 0.116509i −0.897911 0.440176i \(-0.854916\pi\)
0.946171 + 0.323667i \(0.104916\pi\)
\(20\) 1.08617 + 10.5342i 0.0543083 + 0.526708i
\(21\) 3.64718 + 8.80506i 0.173675 + 0.419289i
\(22\) −20.2607 12.0809i −0.920940 0.549133i
\(23\) 8.67649 8.67649i 0.377239 0.377239i −0.492866 0.870105i \(-0.664051\pi\)
0.870105 + 0.492866i \(0.164051\pi\)
\(24\) 13.8441 + 0.584991i 0.576836 + 0.0243746i
\(25\) −12.7214 + 12.7214i −0.508855 + 0.508855i
\(26\) 0.795588 + 3.14564i 0.0305995 + 0.120986i
\(27\) 1.98848 + 4.80062i 0.0736475 + 0.177801i
\(28\) −19.3633 + 10.4640i −0.691546 + 0.373713i
\(29\) −13.5168 + 32.6324i −0.466097 + 1.12526i 0.499756 + 0.866166i \(0.333423\pi\)
−0.965853 + 0.259091i \(0.916577\pi\)
\(30\) −5.48011 7.35388i −0.182670 0.245129i
\(31\) 24.1021i 0.777486i 0.921346 + 0.388743i \(0.127091\pi\)
−0.921346 + 0.388743i \(0.872909\pi\)
\(32\) 1.93531 + 31.9414i 0.0604783 + 0.998170i
\(33\) 20.4287 0.619053
\(34\) −16.9199 + 12.6087i −0.497645 + 0.370844i
\(35\) 13.4588 + 5.57484i 0.384538 + 0.159281i
\(36\) −10.5571 + 5.70508i −0.293252 + 0.158474i
\(37\) −56.6116 + 23.4493i −1.53004 + 0.633764i −0.979573 0.201091i \(-0.935551\pi\)
−0.550470 + 0.834855i \(0.685551\pi\)
\(38\) −4.64583 + 1.17501i −0.122259 + 0.0309214i
\(39\) −1.98696 1.98696i −0.0509477 0.0509477i
\(40\) 15.5955 14.3309i 0.389886 0.358272i
\(41\) −52.9112 52.9112i −1.29052 1.29052i −0.934466 0.356052i \(-0.884123\pi\)
−0.356052 0.934466i \(-0.615877\pi\)
\(42\) 9.76195 16.3716i 0.232427 0.389799i
\(43\) 65.1237 26.9751i 1.51451 0.627329i 0.538024 0.842930i \(-0.319171\pi\)
0.976482 + 0.215601i \(0.0691710\pi\)
\(44\) 4.83884 + 46.9293i 0.109974 + 1.06658i
\(45\) 7.33791 + 3.03946i 0.163065 + 0.0675436i
\(46\) −24.2834 3.54539i −0.527899 0.0770738i
\(47\) −45.0745 −0.959033 −0.479516 0.877533i \(-0.659188\pi\)
−0.479516 + 0.877533i \(0.659188\pi\)
\(48\) −15.6064 22.9006i −0.325134 0.477097i
\(49\) 18.7230i 0.382102i
\(50\) 35.6040 + 5.19822i 0.712080 + 0.103964i
\(51\) 6.99325 16.8832i 0.137122 0.331043i
\(52\) 4.09385 5.03513i 0.0787279 0.0968294i
\(53\) −0.762732 1.84140i −0.0143912 0.0347434i 0.916521 0.399987i \(-0.130986\pi\)
−0.930912 + 0.365244i \(0.880986\pi\)
\(54\) 5.32233 8.92597i 0.0985616 0.165296i
\(55\) 22.0801 22.0801i 0.401457 0.401457i
\(56\) 39.9214 + 18.5475i 0.712882 + 0.331206i
\(57\) 2.93456 2.93456i 0.0514836 0.0514836i
\(58\) 68.4857 17.3212i 1.18079 0.298642i
\(59\) −19.2287 46.4222i −0.325910 0.786817i −0.998888 0.0471538i \(-0.984985\pi\)
0.672977 0.739663i \(-0.265015\pi\)
\(60\) −5.24423 + 17.5768i −0.0874039 + 0.292946i
\(61\) −12.5097 + 30.2011i −0.205077 + 0.495100i −0.992635 0.121140i \(-0.961345\pi\)
0.787558 + 0.616240i \(0.211345\pi\)
\(62\) 38.6522 28.8036i 0.623422 0.464574i
\(63\) 16.5074i 0.262022i
\(64\) 48.9113 41.2758i 0.764238 0.644934i
\(65\) −4.29516 −0.0660795
\(66\) −24.4137 32.7613i −0.369905 0.496384i
\(67\) 105.419 + 43.6660i 1.57342 + 0.651731i 0.987353 0.158534i \(-0.0506768\pi\)
0.586064 + 0.810265i \(0.300677\pi\)
\(68\) 40.4409 + 12.0660i 0.594719 + 0.177441i
\(69\) 19.6352 8.13316i 0.284568 0.117872i
\(70\) −7.14393 28.2461i −0.102056 0.403516i
\(71\) −91.7160 91.7160i −1.29178 1.29178i −0.933688 0.358087i \(-0.883429\pi\)
−0.358087 0.933688i \(-0.616571\pi\)
\(72\) 21.7656 + 10.1123i 0.302300 + 0.140449i
\(73\) −67.6747 67.6747i −0.927050 0.927050i 0.0704643 0.997514i \(-0.477552\pi\)
−0.997514 + 0.0704643i \(0.977552\pi\)
\(74\) 105.260 + 62.7638i 1.42243 + 0.848160i
\(75\) −28.7889 + 11.9248i −0.383852 + 0.158997i
\(76\) 7.43644 + 6.04625i 0.0978479 + 0.0795559i
\(77\) 59.9588 + 24.8357i 0.778685 + 0.322542i
\(78\) −0.811914 + 5.56102i −0.0104091 + 0.0712951i
\(79\) −74.7323 −0.945978 −0.472989 0.881068i \(-0.656825\pi\)
−0.472989 + 0.881068i \(0.656825\pi\)
\(80\) −41.6199 7.88386i −0.520249 0.0985483i
\(81\) 9.00000i 0.111111i
\(82\) −21.6206 + 148.086i −0.263666 + 1.80592i
\(83\) −33.8502 + 81.7215i −0.407833 + 0.984597i 0.577873 + 0.816126i \(0.303883\pi\)
−0.985707 + 0.168470i \(0.946117\pi\)
\(84\) −37.9211 + 3.91000i −0.451441 + 0.0465477i
\(85\) −10.6894 25.8065i −0.125758 0.303606i
\(86\) −121.087 72.2011i −1.40799 0.839547i
\(87\) −43.2593 + 43.2593i −0.497234 + 0.497234i
\(88\) 69.4773 63.8437i 0.789515 0.725497i
\(89\) −9.53321 + 9.53321i −0.107115 + 0.107115i −0.758633 0.651518i \(-0.774132\pi\)
0.651518 + 0.758633i \(0.274132\pi\)
\(90\) −3.89495 15.4001i −0.0432772 0.171112i
\(91\) −3.41617 8.24737i −0.0375404 0.0906305i
\(92\) 23.3346 + 43.1799i 0.253636 + 0.469347i
\(93\) −15.9755 + 38.5683i −0.171780 + 0.414713i
\(94\) 53.8671 + 72.2855i 0.573054 + 0.768994i
\(95\) 6.34357i 0.0667745i
\(96\) −18.0748 + 52.3956i −0.188279 + 0.545788i
\(97\) 92.4092 0.952672 0.476336 0.879263i \(-0.341965\pi\)
0.476336 + 0.879263i \(0.341965\pi\)
\(98\) −30.0258 + 22.3752i −0.306386 + 0.228319i
\(99\) 32.6902 + 13.5407i 0.330204 + 0.136775i
\(100\) −34.2129 63.3099i −0.342129 0.633099i
\(101\) 151.118 62.5953i 1.49622 0.619756i 0.523562 0.851988i \(-0.324603\pi\)
0.972660 + 0.232232i \(0.0746029\pi\)
\(102\) −35.4328 + 8.96156i −0.347380 + 0.0878584i
\(103\) 48.5304 + 48.5304i 0.471169 + 0.471169i 0.902293 0.431124i \(-0.141883\pi\)
−0.431124 + 0.902293i \(0.641883\pi\)
\(104\) −12.9672 0.547939i −0.124685 0.00526865i
\(105\) 17.8418 + 17.8418i 0.169922 + 0.169922i
\(106\) −2.04151 + 3.42378i −0.0192595 + 0.0322998i
\(107\) −114.656 + 47.4923i −1.07156 + 0.443853i −0.847539 0.530732i \(-0.821917\pi\)
−0.224016 + 0.974585i \(0.571917\pi\)
\(108\) −20.6750 + 2.13178i −0.191435 + 0.0197387i
\(109\) 39.5308 + 16.3742i 0.362668 + 0.150222i 0.556574 0.830798i \(-0.312116\pi\)
−0.193906 + 0.981020i \(0.562116\pi\)
\(110\) −61.7969 9.02241i −0.561790 0.0820219i
\(111\) −106.133 −0.956153
\(112\) −17.9643 86.1870i −0.160396 0.769527i
\(113\) 77.7410i 0.687974i −0.938974 0.343987i \(-0.888222\pi\)
0.938974 0.343987i \(-0.111778\pi\)
\(114\) −8.21312 1.19912i −0.0720449 0.0105186i
\(115\) 12.4318 30.0131i 0.108103 0.260983i
\(116\) −109.623 89.1297i −0.945025 0.768360i
\(117\) −1.86254 4.49656i −0.0159191 0.0384321i
\(118\) −51.4671 + 86.3145i −0.436162 + 0.731478i
\(119\) 41.0506 41.0506i 0.344963 0.344963i
\(120\) 34.4548 12.5953i 0.287124 0.104961i
\(121\) 12.8065 12.8065i 0.105839 0.105839i
\(122\) 63.3831 16.0307i 0.519534 0.131399i
\(123\) −49.5979 119.740i −0.403235 0.973495i
\(124\) −92.3839 27.5638i −0.745031 0.222289i
\(125\) −43.5563 + 105.154i −0.348450 + 0.841233i
\(126\) 26.4727 19.7274i 0.210100 0.156567i
\(127\) 191.794i 1.51019i 0.655617 + 0.755094i \(0.272409\pi\)
−0.655617 + 0.755094i \(0.727591\pi\)
\(128\) −124.646 29.1111i −0.973794 0.227430i
\(129\) 122.091 0.946444
\(130\) 5.13301 + 6.88810i 0.0394847 + 0.0529854i
\(131\) 95.7902 + 39.6776i 0.731223 + 0.302883i 0.717055 0.697017i \(-0.245490\pi\)
0.0141686 + 0.999900i \(0.495490\pi\)
\(132\) −23.3629 + 78.3039i −0.176992 + 0.593212i
\(133\) 12.1806 5.04538i 0.0915837 0.0379352i
\(134\) −55.9562 221.243i −0.417583 1.65107i
\(135\) 9.72754 + 9.72754i 0.0720558 + 0.0720558i
\(136\) −28.9794 79.2742i −0.213084 0.582899i
\(137\) 55.9867 + 55.9867i 0.408662 + 0.408662i 0.881272 0.472610i \(-0.156688\pi\)
−0.472610 + 0.881272i \(0.656688\pi\)
\(138\) −36.5084 21.7690i −0.264554 0.157747i
\(139\) 16.0665 6.65497i 0.115587 0.0478775i −0.324141 0.946009i \(-0.605075\pi\)
0.439727 + 0.898131i \(0.355075\pi\)
\(140\) −36.7604 + 45.2126i −0.262575 + 0.322947i
\(141\) −72.1285 29.8766i −0.511550 0.211891i
\(142\) −37.4771 + 256.691i −0.263923 + 1.80768i
\(143\) −19.1348 −0.133810
\(144\) −9.79434 46.9901i −0.0680162 0.326320i
\(145\) 93.5126i 0.644915i
\(146\) −27.6533 + 189.405i −0.189406 + 1.29729i
\(147\) 12.4101 29.9607i 0.0844225 0.203814i
\(148\) −25.1391 243.811i −0.169859 1.64737i
\(149\) 0.236162 + 0.570145i 0.00158498 + 0.00382647i 0.924670 0.380769i \(-0.124341\pi\)
−0.923085 + 0.384596i \(0.874341\pi\)
\(150\) 53.5282 + 31.9175i 0.356855 + 0.212783i
\(151\) 156.583 156.583i 1.03698 1.03698i 0.0376866 0.999290i \(-0.488001\pi\)
0.999290 0.0376866i \(-0.0119989\pi\)
\(152\) 0.809257 19.1514i 0.00532406 0.125996i
\(153\) 22.3813 22.3813i 0.146283 0.146283i
\(154\) −31.8260 125.836i −0.206662 0.817114i
\(155\) 24.4191 + 58.9530i 0.157543 + 0.380342i
\(156\) 9.88843 5.34373i 0.0633874 0.0342547i
\(157\) −33.6759 + 81.3008i −0.214496 + 0.517840i −0.994104 0.108428i \(-0.965418\pi\)
0.779608 + 0.626268i \(0.215418\pi\)
\(158\) 89.3101 + 119.847i 0.565254 + 0.758527i
\(159\) 3.45218i 0.0217118i
\(160\) 37.0953 + 76.1671i 0.231846 + 0.476044i
\(161\) 67.5174 0.419363
\(162\) 14.4332 10.7556i 0.0890938 0.0663926i
\(163\) −87.1420 36.0954i −0.534614 0.221444i 0.0990090 0.995087i \(-0.468433\pi\)
−0.633623 + 0.773642i \(0.718433\pi\)
\(164\) 263.321 142.299i 1.60562 0.867680i
\(165\) 49.9681 20.6975i 0.302837 0.125439i
\(166\) 171.509 43.3776i 1.03319 0.261311i
\(167\) 97.6589 + 97.6589i 0.584784 + 0.584784i 0.936214 0.351430i \(-0.114305\pi\)
−0.351430 + 0.936214i \(0.614305\pi\)
\(168\) 51.5887 + 56.1409i 0.307075 + 0.334172i
\(169\) −117.640 117.640i −0.696094 0.696094i
\(170\) −28.6111 + 47.9830i −0.168300 + 0.282253i
\(171\) 6.64102 2.75080i 0.0388363 0.0160865i
\(172\) 28.9191 + 280.471i 0.168134 + 1.63064i
\(173\) 238.848 + 98.9342i 1.38063 + 0.571874i 0.944649 0.328083i \(-0.106403\pi\)
0.435978 + 0.899957i \(0.356403\pi\)
\(174\) 121.072 + 17.6767i 0.695818 + 0.101590i
\(175\) −98.9932 −0.565676
\(176\) −185.415 35.1224i −1.05350 0.199559i
\(177\) 87.0304i 0.491697i
\(178\) 26.6811 + 3.89547i 0.149894 + 0.0218846i
\(179\) −52.2425 + 126.125i −0.291858 + 0.704607i −0.999999 0.00146404i \(-0.999534\pi\)
0.708141 + 0.706071i \(0.249534\pi\)
\(180\) −20.0422 + 24.6504i −0.111346 + 0.136947i
\(181\) −112.489 271.572i −0.621486 1.50040i −0.849959 0.526849i \(-0.823373\pi\)
0.228473 0.973550i \(-0.426627\pi\)
\(182\) −9.14365 + 15.3346i −0.0502399 + 0.0842562i
\(183\) −40.0362 + 40.0362i −0.218777 + 0.218777i
\(184\) 41.3608 89.0243i 0.224787 0.483828i
\(185\) −114.713 + 114.713i −0.620068 + 0.620068i
\(186\) 80.9433 20.4720i 0.435179 0.110064i
\(187\) −47.6211 114.967i −0.254658 0.614799i
\(188\) 51.5486 172.772i 0.274194 0.919000i
\(189\) −10.9415 + 26.4152i −0.0578917 + 0.139763i
\(190\) −10.1731 + 7.58100i −0.0535427 + 0.0399000i
\(191\) 120.132i 0.628961i −0.949264 0.314480i \(-0.898170\pi\)
0.949264 0.314480i \(-0.101830\pi\)
\(192\) 105.627 33.6300i 0.550140 0.175156i
\(193\) 101.136 0.524018 0.262009 0.965065i \(-0.415615\pi\)
0.262009 + 0.965065i \(0.415615\pi\)
\(194\) −110.435 148.196i −0.569254 0.763894i
\(195\) −6.87315 2.84695i −0.0352469 0.0145998i
\(196\) 71.7658 + 21.4122i 0.366152 + 0.109246i
\(197\) 131.690 54.5477i 0.668476 0.276892i −0.0225242 0.999746i \(-0.507170\pi\)
0.691000 + 0.722854i \(0.257170\pi\)
\(198\) −17.3519 68.6069i −0.0876358 0.346500i
\(199\) −46.8247 46.8247i −0.235300 0.235300i 0.579601 0.814901i \(-0.303209\pi\)
−0.814901 + 0.579601i \(0.803209\pi\)
\(200\) −60.6427 + 130.526i −0.303214 + 0.652632i
\(201\) 139.749 + 139.749i 0.695269 + 0.695269i
\(202\) −280.980 167.541i −1.39099 0.829412i
\(203\) −179.559 + 74.3756i −0.884525 + 0.366382i
\(204\) 56.7161 + 46.1134i 0.278020 + 0.226046i
\(205\) −183.027 75.8121i −0.892813 0.369815i
\(206\) 19.8305 135.825i 0.0962648 0.659344i
\(207\) 36.8112 0.177832
\(208\) 14.6180 + 21.4502i 0.0702786 + 0.103126i
\(209\) 28.2604i 0.135217i
\(210\) 7.29052 49.9348i 0.0347168 0.237785i
\(211\) 8.54819 20.6372i 0.0405128 0.0978065i −0.902328 0.431050i \(-0.858143\pi\)
0.942841 + 0.333244i \(0.108143\pi\)
\(212\) 7.93042 0.817697i 0.0374076 0.00385706i
\(213\) −85.9727 207.556i −0.403628 0.974443i
\(214\) 213.185 + 127.117i 0.996191 + 0.594004i
\(215\) 131.961 131.961i 0.613771 0.613771i
\(216\) 28.1267 + 30.6086i 0.130216 + 0.141707i
\(217\) −93.7769 + 93.7769i −0.432151 + 0.432151i
\(218\) −20.9829 82.9634i −0.0962517 0.380566i
\(219\) −63.4368 153.150i −0.289666 0.699315i
\(220\) 59.3823 + 109.885i 0.269920 + 0.499479i
\(221\) −6.55031 + 15.8138i −0.0296394 + 0.0715559i
\(222\) 126.836 + 170.204i 0.571333 + 0.766685i
\(223\) 88.1855i 0.395451i 0.980257 + 0.197725i \(0.0633554\pi\)
−0.980257 + 0.197725i \(0.936645\pi\)
\(224\) −116.748 + 131.808i −0.521199 + 0.588430i
\(225\) −53.9722 −0.239877
\(226\) −124.672 + 92.9057i −0.551647 + 0.411087i
\(227\) 198.836 + 82.3607i 0.875931 + 0.362822i 0.774917 0.632063i \(-0.217792\pi\)
0.101013 + 0.994885i \(0.467792\pi\)
\(228\) 7.89221 + 14.6043i 0.0346150 + 0.0640540i
\(229\) −302.608 + 125.344i −1.32143 + 0.547355i −0.928199 0.372084i \(-0.878643\pi\)
−0.393233 + 0.919439i \(0.628643\pi\)
\(230\) −62.9885 + 15.9309i −0.273863 + 0.0692647i
\(231\) 79.4846 + 79.4846i 0.344089 + 0.344089i
\(232\) −11.9295 + 282.317i −0.0514203 + 1.21688i
\(233\) −63.3477 63.3477i −0.271878 0.271878i 0.557978 0.829856i \(-0.311577\pi\)
−0.829856 + 0.557978i \(0.811577\pi\)
\(234\) −4.98522 + 8.36062i −0.0213044 + 0.0357291i
\(235\) −110.251 + 45.6675i −0.469153 + 0.194330i
\(236\) 199.928 20.6144i 0.847153 0.0873491i
\(237\) −119.587 49.5346i −0.504587 0.209007i
\(238\) −114.891 16.7741i −0.482734 0.0704796i
\(239\) 130.238 0.544928 0.272464 0.962166i \(-0.412161\pi\)
0.272464 + 0.962166i \(0.412161\pi\)
\(240\) −61.3748 40.2026i −0.255728 0.167511i
\(241\) 307.946i 1.27778i 0.769297 + 0.638892i \(0.220607\pi\)
−0.769297 + 0.638892i \(0.779393\pi\)
\(242\) −35.8422 5.23299i −0.148108 0.0216239i
\(243\) −5.96544 + 14.4019i −0.0245492 + 0.0592669i
\(244\) −101.455 82.4890i −0.415800 0.338069i
\(245\) −18.9693 45.7959i −0.0774257 0.186922i
\(246\) −132.753 + 222.637i −0.539645 + 0.905027i
\(247\) −2.74870 + 2.74870i −0.0111283 + 0.0111283i
\(248\) 66.2012 + 181.096i 0.266940 + 0.730224i
\(249\) −108.334 + 108.334i −0.435078 + 0.435078i
\(250\) 220.687 55.8156i 0.882748 0.223262i
\(251\) −81.4850 196.722i −0.324642 0.783754i −0.998972 0.0453246i \(-0.985568\pi\)
0.674331 0.738429i \(-0.264432\pi\)
\(252\) −63.2732 18.8783i −0.251084 0.0749139i
\(253\) 55.3834 133.707i 0.218907 0.528488i
\(254\) 307.577 229.206i 1.21093 0.902388i
\(255\) 48.3810i 0.189730i
\(256\) 102.275 + 234.682i 0.399511 + 0.916728i
\(257\) −328.067 −1.27653 −0.638263 0.769818i \(-0.720347\pi\)
−0.638263 + 0.769818i \(0.720347\pi\)
\(258\) −145.907 195.796i −0.565532 0.758900i
\(259\) −311.502 129.029i −1.20271 0.498180i
\(260\) 4.91208 16.4635i 0.0188926 0.0633211i
\(261\) −97.8973 + 40.5504i −0.375086 + 0.155366i
\(262\) −50.8452 201.035i −0.194066 0.767309i
\(263\) 179.992 + 179.992i 0.684380 + 0.684380i 0.960984 0.276604i \(-0.0892091\pi\)
−0.276604 + 0.960984i \(0.589209\pi\)
\(264\) 153.495 56.1117i 0.581422 0.212544i
\(265\) −3.73124 3.73124i −0.0140802 0.0140802i
\(266\) −22.6479 13.5044i −0.0851424 0.0507683i
\(267\) −21.5740 + 8.93623i −0.0808014 + 0.0334690i
\(268\) −287.933 + 354.136i −1.07438 + 1.32140i
\(269\) −222.886 92.3226i −0.828574 0.343207i −0.0722361 0.997388i \(-0.523014\pi\)
−0.756338 + 0.654181i \(0.773014\pi\)
\(270\) 3.97487 27.2250i 0.0147218 0.100833i
\(271\) 259.013 0.955769 0.477884 0.878423i \(-0.341404\pi\)
0.477884 + 0.878423i \(0.341404\pi\)
\(272\) −92.4987 + 141.212i −0.340069 + 0.519162i
\(273\) 15.4618i 0.0566367i
\(274\) 22.8773 156.693i 0.0834939 0.571873i
\(275\) −81.2025 + 196.040i −0.295282 + 0.712874i
\(276\) 8.71927 + 84.5636i 0.0315915 + 0.306390i
\(277\) −47.6027 114.923i −0.171851 0.414884i 0.814364 0.580354i \(-0.197086\pi\)
−0.986215 + 0.165470i \(0.947086\pi\)
\(278\) −29.8731 17.8126i −0.107457 0.0640739i
\(279\) −51.1282 + 51.1282i −0.183255 + 0.183255i
\(280\) 116.438 + 4.92018i 0.415850 + 0.0175721i
\(281\) −275.219 + 275.219i −0.979427 + 0.979427i −0.999793 0.0203657i \(-0.993517\pi\)
0.0203657 + 0.999793i \(0.493517\pi\)
\(282\) 38.2857 + 151.376i 0.135765 + 0.536795i
\(283\) 88.4398 + 213.512i 0.312508 + 0.754461i 0.999611 + 0.0279008i \(0.00888225\pi\)
−0.687103 + 0.726560i \(0.741118\pi\)
\(284\) 456.439 246.661i 1.60718 0.868525i
\(285\) 4.20469 10.1510i 0.0147533 0.0356176i
\(286\) 22.8674 + 30.6863i 0.0799560 + 0.107295i
\(287\) 411.736i 1.43462i
\(288\) −63.6526 + 71.8634i −0.221016 + 0.249526i
\(289\) 177.684 0.614824
\(290\) 149.965 111.754i 0.517121 0.385358i
\(291\) 147.874 + 61.2513i 0.508157 + 0.210486i
\(292\) 336.794 182.004i 1.15340 0.623302i
\(293\) 203.093 84.1237i 0.693149 0.287112i −0.00816246 0.999967i \(-0.502598\pi\)
0.701311 + 0.712855i \(0.252598\pi\)
\(294\) −62.8785 + 15.9031i −0.213872 + 0.0540920i
\(295\) −94.0657 94.0657i −0.318867 0.318867i
\(296\) −360.954 + 331.686i −1.21944 + 1.12056i
\(297\) 43.3359 + 43.3359i 0.145912 + 0.145912i
\(298\) 0.632105 1.06009i 0.00212116 0.00355735i
\(299\) −18.3915 + 7.61803i −0.0615102 + 0.0254784i
\(300\) −12.7841 123.986i −0.0426136 0.413287i
\(301\) 358.340 + 148.429i 1.19050 + 0.493121i
\(302\) −438.239 63.9832i −1.45112 0.211865i
\(303\) 283.311 0.935018
\(304\) −31.6800 + 21.5894i −0.104210 + 0.0710178i
\(305\) 86.5453i 0.283755i
\(306\) −62.6397 9.14545i −0.204705 0.0298871i
\(307\) 36.3569 87.7733i 0.118426 0.285906i −0.853540 0.521028i \(-0.825549\pi\)
0.971966 + 0.235121i \(0.0755488\pi\)
\(308\) −163.767 + 201.421i −0.531710 + 0.653964i
\(309\) 45.4914 + 109.826i 0.147221 + 0.355424i
\(310\) 65.3597 109.613i 0.210838 0.353592i
\(311\) 177.975 177.975i 0.572268 0.572268i −0.360493 0.932762i \(-0.617392\pi\)
0.932762 + 0.360493i \(0.117392\pi\)
\(312\) −20.3870 9.47183i −0.0653430 0.0303584i
\(313\) 342.829 342.829i 1.09530 1.09530i 0.100347 0.994953i \(-0.468005\pi\)
0.994953 0.100347i \(-0.0319951\pi\)
\(314\) 170.626 43.1543i 0.543395 0.137434i
\(315\) 16.7245 + 40.3765i 0.0530937 + 0.128179i
\(316\) 85.4660 286.451i 0.270462 0.906491i
\(317\) 40.3004 97.2937i 0.127131 0.306920i −0.847480 0.530827i \(-0.821881\pi\)
0.974610 + 0.223907i \(0.0718812\pi\)
\(318\) −5.53621 + 4.12558i −0.0174095 + 0.0129735i
\(319\) 416.596i 1.30594i
\(320\) 77.8168 150.514i 0.243177 0.470356i
\(321\) −214.953 −0.669636
\(322\) −80.6878 108.277i −0.250583 0.336263i
\(323\) −23.3556 9.67422i −0.0723085 0.0299511i
\(324\) −34.4973 10.2927i −0.106473 0.0317675i
\(325\) 26.9655 11.1695i 0.0829707 0.0343676i
\(326\) 46.2548 + 182.885i 0.141886 + 0.560997i
\(327\) 52.4042 + 52.4042i 0.160258 + 0.160258i
\(328\) −542.890 252.228i −1.65515 0.768986i
\(329\) −175.377 175.377i −0.533061 0.533061i
\(330\) −92.9075 55.3984i −0.281538 0.167874i
\(331\) 555.090 229.926i 1.67701 0.694640i 0.677832 0.735217i \(-0.262920\pi\)
0.999176 + 0.0405768i \(0.0129196\pi\)
\(332\) −274.529 223.208i −0.826894 0.672313i
\(333\) −169.835 70.3478i −0.510014 0.211255i
\(334\) 39.9055 273.323i 0.119477 0.818333i
\(335\) 302.092 0.901768
\(336\) 28.3805 149.824i 0.0844658 0.445905i
\(337\) 611.720i 1.81519i 0.419845 + 0.907596i \(0.362084\pi\)
−0.419845 + 0.907596i \(0.637916\pi\)
\(338\) −48.0701 + 329.245i −0.142219 + 0.974099i
\(339\) 51.5289 124.402i 0.152003 0.366967i
\(340\) 111.142 11.4597i 0.326888 0.0337051i
\(341\) 108.786 + 262.634i 0.319022 + 0.770187i
\(342\) −12.3479 7.36273i −0.0361049 0.0215284i
\(343\) 263.498 263.498i 0.768216 0.768216i
\(344\) 415.227 381.559i 1.20706 1.10918i
\(345\) 39.7870 39.7870i 0.115325 0.115325i
\(346\) −126.780 501.271i −0.366417 1.44876i
\(347\) 122.090 + 294.751i 0.351844 + 0.849426i 0.996393 + 0.0848628i \(0.0270452\pi\)
−0.644549 + 0.764563i \(0.722955\pi\)
\(348\) −116.342 215.287i −0.334315 0.618641i
\(349\) 261.168 630.515i 0.748332 1.80663i 0.180329 0.983606i \(-0.442284\pi\)
0.568002 0.823027i \(-0.307716\pi\)
\(350\) 118.304 + 158.754i 0.338010 + 0.453584i
\(351\) 8.42996i 0.0240170i
\(352\) 165.258 + 339.322i 0.469484 + 0.963983i
\(353\) 132.343 0.374910 0.187455 0.982273i \(-0.439976\pi\)
0.187455 + 0.982273i \(0.439976\pi\)
\(354\) −139.570 + 104.007i −0.394264 + 0.293805i
\(355\) −317.257 131.412i −0.893683 0.370175i
\(356\) −25.6386 47.4435i −0.0720186 0.133268i
\(357\) 92.8990 38.4800i 0.260221 0.107787i
\(358\) 264.698 66.9467i 0.739379 0.187002i
\(359\) −244.221 244.221i −0.680280 0.680280i 0.279783 0.960063i \(-0.409737\pi\)
−0.960063 + 0.279783i \(0.909737\pi\)
\(360\) 63.4834 + 2.68254i 0.176343 + 0.00745150i
\(361\) 251.206 + 251.206i 0.695861 + 0.695861i
\(362\) −301.085 + 504.944i −0.831728 + 1.39487i
\(363\) 28.9815 12.0045i 0.0798388 0.0330703i
\(364\) 35.5192 3.66235i 0.0975804 0.0100614i
\(365\) −234.095 96.9654i −0.641357 0.265659i
\(366\) 112.052 + 16.3596i 0.306152 + 0.0446985i
\(367\) −448.004 −1.22072 −0.610359 0.792125i \(-0.708975\pi\)
−0.610359 + 0.792125i \(0.708975\pi\)
\(368\) −192.196 + 40.0602i −0.522272 + 0.108859i
\(369\) 224.483i 0.608356i
\(370\) 321.052 + 46.8739i 0.867709 + 0.126686i
\(371\) 4.19690 10.1322i 0.0113124 0.0273105i
\(372\) −129.563 105.342i −0.348288 0.283178i
\(373\) 190.741 + 460.490i 0.511370 + 1.23456i 0.943087 + 0.332547i \(0.107908\pi\)
−0.431716 + 0.902009i \(0.642092\pi\)
\(374\) −127.461 + 213.763i −0.340806 + 0.571559i
\(375\) −139.398 + 139.398i −0.371728 + 0.371728i
\(376\) −338.676 + 123.806i −0.900735 + 0.329272i
\(377\) 40.5194 40.5194i 0.107479 0.107479i
\(378\) 55.4376 14.0211i 0.146660 0.0370929i
\(379\) 105.816 + 255.464i 0.279199 + 0.674046i 0.999814 0.0192892i \(-0.00614033\pi\)
−0.720615 + 0.693336i \(0.756140\pi\)
\(380\) 24.3151 + 7.25470i 0.0639871 + 0.0190913i
\(381\) −127.126 + 306.910i −0.333664 + 0.805537i
\(382\) −192.653 + 143.565i −0.504328 + 0.375825i
\(383\) 26.0891i 0.0681176i 0.999420 + 0.0340588i \(0.0108434\pi\)
−0.999420 + 0.0340588i \(0.989157\pi\)
\(384\) −180.163 129.202i −0.469175 0.336464i
\(385\) 171.820 0.446285
\(386\) −120.864 162.190i −0.313118 0.420181i
\(387\) 195.371 + 80.9254i 0.504835 + 0.209110i
\(388\) −105.682 + 354.207i −0.272376 + 0.912905i
\(389\) −295.230 + 122.288i −0.758947 + 0.314366i −0.728386 0.685167i \(-0.759729\pi\)
−0.0305609 + 0.999533i \(0.509729\pi\)
\(390\) 3.64825 + 14.4247i 0.00935449 + 0.0369864i
\(391\) −91.5425 91.5425i −0.234124 0.234124i
\(392\) −51.4265 140.679i −0.131190 0.358875i
\(393\) 126.985 + 126.985i 0.323116 + 0.323116i
\(394\) −244.856 146.001i −0.621461 0.370561i
\(395\) −182.793 + 75.7154i −0.462767 + 0.191684i
\(396\) −89.2874 + 109.817i −0.225473 + 0.277315i
\(397\) 356.068 + 147.488i 0.896897 + 0.371507i 0.783026 0.621989i \(-0.213675\pi\)
0.113871 + 0.993496i \(0.463675\pi\)
\(398\) −19.1335 + 131.051i −0.0480742 + 0.329273i
\(399\) 22.8357 0.0572324
\(400\) 281.796 58.7358i 0.704489 0.146839i
\(401\) 316.421i 0.789080i −0.918879 0.394540i \(-0.870904\pi\)
0.918879 0.394540i \(-0.129096\pi\)
\(402\) 57.1044 391.123i 0.142051 0.972944i
\(403\) 14.9637 36.1255i 0.0371307 0.0896413i
\(404\) 67.1062 + 650.827i 0.166104 + 1.61096i
\(405\) 9.11839 + 22.0137i 0.0225145 + 0.0543549i
\(406\) 333.860 + 199.072i 0.822314 + 0.490325i
\(407\) −511.041 + 511.041i −1.25563 + 1.25563i
\(408\) 6.17203 146.063i 0.0151275 0.357999i
\(409\) 105.887 105.887i 0.258893 0.258893i −0.565710 0.824604i \(-0.691398\pi\)
0.824604 + 0.565710i \(0.191398\pi\)
\(410\) 97.1502 + 384.118i 0.236952 + 0.936874i
\(411\) 52.4808 + 126.700i 0.127690 + 0.308272i
\(412\) −241.519 + 130.518i −0.586212 + 0.316791i
\(413\) 105.805 255.436i 0.256187 0.618489i
\(414\) −43.9919 59.0337i −0.106261 0.142594i
\(415\) 234.184i 0.564299i
\(416\) 16.9299 49.0770i 0.0406970 0.117974i
\(417\) 30.1209 0.0722323
\(418\) −45.3209 + 33.7731i −0.108423 + 0.0807969i
\(419\) −228.165 94.5090i −0.544546 0.225559i 0.0934144 0.995627i \(-0.470222\pi\)
−0.637961 + 0.770069i \(0.720222\pi\)
\(420\) −88.7924 + 47.9837i −0.211411 + 0.114247i
\(421\) −274.847 + 113.845i −0.652844 + 0.270417i −0.684424 0.729084i \(-0.739946\pi\)
0.0315798 + 0.999501i \(0.489946\pi\)
\(422\) −43.3112 + 10.9542i −0.102633 + 0.0259577i
\(423\) −95.6175 95.6175i −0.226046 0.226046i
\(424\) −10.7887 11.7407i −0.0254451 0.0276904i
\(425\) 134.219 + 134.219i 0.315808 + 0.315808i
\(426\) −230.113 + 385.917i −0.540170 + 0.905909i
\(427\) −166.180 + 68.8341i −0.389181 + 0.161204i
\(428\) −50.9147 493.795i −0.118960 1.15373i
\(429\) −30.6197 12.6831i −0.0713745 0.0295643i
\(430\) −369.326 53.9219i −0.858898 0.125400i
\(431\) −88.4729 −0.205274 −0.102637 0.994719i \(-0.532728\pi\)
−0.102637 + 0.994719i \(0.532728\pi\)
\(432\) 15.4734 81.6858i 0.0358180 0.189088i
\(433\) 632.415i 1.46054i −0.683157 0.730271i \(-0.739394\pi\)
0.683157 0.730271i \(-0.260606\pi\)
\(434\) 262.458 + 38.3192i 0.604743 + 0.0882930i
\(435\) −61.9827 + 149.640i −0.142489 + 0.343999i
\(436\) −107.971 + 132.797i −0.247641 + 0.304580i
\(437\) −11.2511 27.1627i −0.0257463 0.0621571i
\(438\) −169.794 + 284.757i −0.387657 + 0.650131i
\(439\) −344.094 + 344.094i −0.783812 + 0.783812i −0.980472 0.196660i \(-0.936991\pi\)
0.196660 + 0.980472i \(0.436991\pi\)
\(440\) 105.256 226.551i 0.239218 0.514889i
\(441\) 39.7175 39.7175i 0.0900623 0.0900623i
\(442\) 33.1885 8.39396i 0.0750872 0.0189909i
\(443\) 16.8358 + 40.6453i 0.0380042 + 0.0917502i 0.941742 0.336336i \(-0.109188\pi\)
−0.903738 + 0.428086i \(0.859188\pi\)
\(444\) 121.377 406.811i 0.273371 0.916241i
\(445\) −13.6593 + 32.9766i −0.0306952 + 0.0741047i
\(446\) 141.422 105.388i 0.317090 0.236295i
\(447\) 1.06888i 0.00239124i
\(448\) 350.902 + 29.7083i 0.783263 + 0.0663132i
\(449\) −712.697 −1.58730 −0.793649 0.608376i \(-0.791821\pi\)
−0.793649 + 0.608376i \(0.791821\pi\)
\(450\) 64.5004 + 86.5546i 0.143334 + 0.192344i
\(451\) −815.378 337.741i −1.80793 0.748871i
\(452\) 297.984 + 88.9069i 0.659256 + 0.196697i
\(453\) 354.353 146.778i 0.782237 0.324013i
\(454\) −105.542 417.298i −0.232471 0.919158i
\(455\) −16.7117 16.7117i −0.0367291 0.0367291i
\(456\) 13.9890 30.1098i 0.0306777 0.0660302i
\(457\) −215.306 215.306i −0.471129 0.471129i 0.431151 0.902280i \(-0.358108\pi\)
−0.902280 + 0.431151i \(0.858108\pi\)
\(458\) 562.650 + 335.494i 1.22849 + 0.732519i
\(459\) 50.6496 20.9797i 0.110348 0.0457075i
\(460\) 100.824 + 81.9754i 0.219182 + 0.178207i
\(461\) −476.683 197.449i −1.03402 0.428305i −0.199858 0.979825i \(-0.564048\pi\)
−0.834162 + 0.551520i \(0.814048\pi\)
\(462\) 32.4791 222.458i 0.0703010 0.481511i
\(463\) −369.088 −0.797167 −0.398584 0.917132i \(-0.630498\pi\)
−0.398584 + 0.917132i \(0.630498\pi\)
\(464\) 467.005 318.256i 1.00648 0.685897i
\(465\) 110.523i 0.237683i
\(466\) −25.8852 + 177.295i −0.0555476 + 0.380460i
\(467\) 266.802 644.117i 0.571310 1.37926i −0.329130 0.944285i \(-0.606755\pi\)
0.900440 0.434980i \(-0.143245\pi\)
\(468\) 19.3655 1.99676i 0.0413793 0.00426657i
\(469\) 240.270 + 580.063i 0.512303 + 1.23681i
\(470\) 204.994 + 122.233i 0.436157 + 0.260069i
\(471\) −107.777 + 107.777i −0.228825 + 0.228825i
\(472\) −271.987 295.987i −0.576243 0.627090i
\(473\) 587.882 587.882i 1.24288 1.24288i
\(474\) 63.4766 + 250.978i 0.133917 + 0.529488i
\(475\) 16.4963 + 39.8256i 0.0347291 + 0.0838434i
\(476\) 110.402 + 204.295i 0.231936 + 0.429191i
\(477\) 2.28820 5.52420i 0.00479706 0.0115811i
\(478\) −155.643 208.861i −0.325613 0.436947i
\(479\) 378.016i 0.789178i −0.918858 0.394589i \(-0.870887\pi\)
0.918858 0.394589i \(-0.129113\pi\)
\(480\) 8.87455 + 146.471i 0.0184887 + 0.305147i
\(481\) 99.4108 0.206675
\(482\) 493.849 368.016i 1.02458 0.763518i
\(483\) 108.042 + 44.7524i 0.223689 + 0.0926550i
\(484\) 34.4417 + 63.7334i 0.0711606 + 0.131681i
\(485\) 226.030 93.6248i 0.466042 0.193041i
\(486\) 30.2252 7.64447i 0.0621917 0.0157294i
\(487\) −222.455 222.455i −0.456786 0.456786i 0.440813 0.897599i \(-0.354690\pi\)
−0.897599 + 0.440813i \(0.854690\pi\)
\(488\) −11.0407 + 261.282i −0.0226244 + 0.535415i
\(489\) −115.520 115.520i −0.236238 0.236238i
\(490\) −50.7728 + 85.1500i −0.103618 + 0.173776i
\(491\) 23.4533 9.71469i 0.0477665 0.0197855i −0.358672 0.933464i \(-0.616770\pi\)
0.406439 + 0.913678i \(0.366770\pi\)
\(492\) 515.688 53.1721i 1.04815 0.108073i
\(493\) 344.293 + 142.611i 0.698363 + 0.289271i
\(494\) 7.69293 + 1.12317i 0.0155727 + 0.00227363i
\(495\) 93.6781 0.189249
\(496\) 211.306 322.587i 0.426020 0.650378i
\(497\) 713.702i 1.43602i
\(498\) 303.202 + 44.2677i 0.608839 + 0.0888910i
\(499\) −167.053 + 403.300i −0.334775 + 0.808217i 0.663425 + 0.748242i \(0.269102\pi\)
−0.998200 + 0.0599748i \(0.980898\pi\)
\(500\) −353.247 287.210i −0.706493 0.574420i
\(501\) 91.5434 + 221.005i 0.182721 + 0.441128i
\(502\) −218.101 + 365.773i −0.434464 + 0.728631i
\(503\) −475.486 + 475.486i −0.945300 + 0.945300i −0.998580 0.0532793i \(-0.983033\pi\)
0.0532793 + 0.998580i \(0.483033\pi\)
\(504\) 45.3408 + 124.031i 0.0899619 + 0.246094i
\(505\) 306.213 306.213i 0.606362 0.606362i
\(506\) −280.612 + 70.9716i −0.554569 + 0.140260i
\(507\) −110.273 266.223i −0.217501 0.525095i
\(508\) −735.151 219.341i −1.44715 0.431774i
\(509\) −122.245 + 295.125i −0.240167 + 0.579814i −0.997299 0.0734479i \(-0.976600\pi\)
0.757132 + 0.653261i \(0.226600\pi\)
\(510\) −77.5881 + 57.8186i −0.152133 + 0.113370i
\(511\) 526.620i 1.03057i
\(512\) 254.132 444.478i 0.496352 0.868122i
\(513\) 12.4503 0.0242696
\(514\) 392.062 + 526.118i 0.762767 + 1.02357i
\(515\) 167.873 + 69.5352i 0.325967 + 0.135020i
\(516\) −139.627 + 467.979i −0.270595 + 0.906937i
\(517\) −491.165 + 203.447i −0.950029 + 0.393515i
\(518\) 165.345 + 653.751i 0.319199 + 1.26207i
\(519\) 316.630 + 316.630i 0.610078 + 0.610078i
\(520\) −32.2726 + 11.7975i −0.0620626 + 0.0226876i
\(521\) 621.839 + 621.839i 1.19355 + 1.19355i 0.976064 + 0.217486i \(0.0697855\pi\)
0.217486 + 0.976064i \(0.430215\pi\)
\(522\) 182.024 + 108.536i 0.348705 + 0.207924i
\(523\) 348.756 144.459i 0.666837 0.276213i −0.0234751 0.999724i \(-0.507473\pi\)
0.690312 + 0.723511i \(0.257473\pi\)
\(524\) −261.634 + 321.790i −0.499301 + 0.614104i
\(525\) −158.410 65.6154i −0.301733 0.124982i
\(526\) 73.5484 503.753i 0.139826 0.957706i
\(527\) 254.292 0.482527
\(528\) −273.423 179.101i −0.517846 0.339207i
\(529\) 378.437i 0.715382i
\(530\) −1.52466 + 10.4428i −0.00287672 + 0.0197035i
\(531\) 57.6861 139.267i 0.108637 0.262272i
\(532\) 5.40897 + 52.4587i 0.0101672 + 0.0986067i
\(533\) 46.4565 + 112.156i 0.0871604 + 0.210424i
\(534\) 40.1133 + 23.9185i 0.0751185 + 0.0447912i
\(535\) −232.330 + 232.330i −0.434261 + 0.434261i
\(536\) 912.023 + 38.5383i 1.70154 + 0.0718997i
\(537\) −167.198 + 167.198i −0.311355 + 0.311355i
\(538\) 118.308 + 467.772i 0.219903 + 0.869465i
\(539\) −84.5076 204.019i −0.156786 0.378515i
\(540\) −48.4106 + 26.1612i −0.0896493 + 0.0484467i
\(541\) 111.084 268.182i 0.205332 0.495715i −0.787345 0.616512i \(-0.788545\pi\)
0.992677 + 0.120797i \(0.0385451\pi\)
\(542\) −309.538 415.377i −0.571104 0.766377i
\(543\) 509.132i 0.937629i
\(544\) 337.002 20.4187i 0.619489 0.0375344i
\(545\) 113.281 0.207855
\(546\) −24.7959 + 18.4779i −0.0454138 + 0.0338423i
\(547\) 76.5752 + 31.7185i 0.139991 + 0.0579862i 0.451579 0.892231i \(-0.350861\pi\)
−0.311588 + 0.950217i \(0.600861\pi\)
\(548\) −278.627 + 150.571i −0.508443 + 0.274764i
\(549\) −90.6033 + 37.5291i −0.165033 + 0.0683591i
\(550\) 411.430 104.058i 0.748054 0.189196i
\(551\) 59.8435 + 59.8435i 0.108609 + 0.108609i
\(552\) 125.193 115.042i 0.226800 0.208410i
\(553\) −290.770 290.770i −0.525805 0.525805i
\(554\) −127.412 + 213.680i −0.229986 + 0.385705i
\(555\) −259.598 + 107.529i −0.467745 + 0.193746i
\(556\) 7.13456 + 69.1943i 0.0128319 + 0.124450i
\(557\) 575.171 + 238.244i 1.03262 + 0.427726i 0.833658 0.552281i \(-0.186242\pi\)
0.198964 + 0.980007i \(0.436242\pi\)
\(558\) 143.095 + 20.8920i 0.256443 + 0.0374409i
\(559\) −114.358 −0.204577
\(560\) −131.261 192.610i −0.234394 0.343947i
\(561\) 215.536i 0.384200i
\(562\) 770.270 + 112.460i 1.37059 + 0.200107i
\(563\) 213.668 515.840i 0.379517 0.916235i −0.612539 0.790440i \(-0.709852\pi\)
0.992056 0.125795i \(-0.0401482\pi\)
\(564\) 197.006 242.303i 0.349302 0.429615i
\(565\) −78.7637 190.152i −0.139405 0.336553i
\(566\) 236.716 396.992i 0.418226 0.701398i
\(567\) −35.0174 + 35.0174i −0.0617591 + 0.0617591i
\(568\) −941.043 437.210i −1.65677 0.769735i
\(569\) −14.5552 + 14.5552i −0.0255804 + 0.0255804i −0.719781 0.694201i \(-0.755758\pi\)
0.694201 + 0.719781i \(0.255758\pi\)
\(570\) −21.3040 + 5.38814i −0.0373754 + 0.00945288i
\(571\) 345.000 + 832.905i 0.604204 + 1.45868i 0.869216 + 0.494432i \(0.164624\pi\)
−0.265013 + 0.964245i \(0.585376\pi\)
\(572\) 21.8832 73.3444i 0.0382573 0.128224i
\(573\) 79.6264 192.235i 0.138964 0.335489i
\(574\) −660.297 + 492.053i −1.15034 + 0.857235i
\(575\) 220.754i 0.383920i
\(576\) 191.316 + 16.1973i 0.332145 + 0.0281203i
\(577\) −1014.06 −1.75747 −0.878734 0.477312i \(-0.841611\pi\)
−0.878734 + 0.477312i \(0.841611\pi\)
\(578\) −212.345 284.950i −0.367378 0.492993i
\(579\) 161.838 + 67.0354i 0.279512 + 0.115778i
\(580\) −358.437 106.944i −0.617994 0.184386i
\(581\) −449.669 + 186.259i −0.773957 + 0.320583i
\(582\) −78.4911 310.343i −0.134864 0.533235i
\(583\) −16.6226 16.6226i −0.0285121 0.0285121i
\(584\) −694.369 322.605i −1.18899 0.552405i
\(585\) −9.11142 9.11142i −0.0155751 0.0155751i
\(586\) −377.618 225.164i −0.644399 0.384238i
\(587\) 999.121 413.849i 1.70208 0.705024i 0.702104 0.712074i \(-0.252244\pi\)
0.999975 + 0.00704949i \(0.00224394\pi\)
\(588\) 100.648 + 81.8322i 0.171169 + 0.139170i
\(589\) 53.3541 + 22.1000i 0.0905841 + 0.0375212i
\(590\) −38.4372 + 263.267i −0.0651478 + 0.446215i
\(591\) 246.887 0.417744
\(592\) 963.285 + 182.470i 1.62717 + 0.308227i
\(593\) 446.986i 0.753770i 0.926260 + 0.376885i \(0.123005\pi\)
−0.926260 + 0.376885i \(0.876995\pi\)
\(594\) 17.7079 121.287i 0.0298114 0.204186i
\(595\) 58.8181 141.999i 0.0988539 0.238654i
\(596\) −2.45546 + 0.253180i −0.00411990 + 0.000424799i
\(597\) −43.8925 105.966i −0.0735217 0.177497i
\(598\) 34.1961 + 20.3902i 0.0571841 + 0.0340974i
\(599\) −620.335 + 620.335i −1.03562 + 1.03562i −0.0362765 + 0.999342i \(0.511550\pi\)
−0.999342 + 0.0362765i \(0.988450\pi\)
\(600\) −183.557 + 168.673i −0.305929 + 0.281122i
\(601\) 182.515 182.515i 0.303686 0.303686i −0.538768 0.842454i \(-0.681110\pi\)
0.842454 + 0.538768i \(0.181110\pi\)
\(602\) −190.206 752.049i −0.315957 1.24925i
\(603\) 130.998 + 316.257i 0.217244 + 0.524472i
\(604\) 421.115 + 779.262i 0.697211 + 1.29017i
\(605\) 18.3493 44.2992i 0.0303295 0.0732218i
\(606\) −338.575 454.342i −0.558705 0.749739i
\(607\) 304.396i 0.501476i −0.968055 0.250738i \(-0.919327\pi\)
0.968055 0.250738i \(-0.0806732\pi\)
\(608\) 72.4824 + 25.0040i 0.119214 + 0.0411250i
\(609\) −336.629 −0.552757
\(610\) 138.792 103.427i 0.227527 0.169553i
\(611\) 67.5601 + 27.9843i 0.110573 + 0.0458008i
\(612\) 60.1922 + 111.384i 0.0983532 + 0.182000i
\(613\) −273.964 + 113.479i −0.446923 + 0.185121i −0.594782 0.803887i \(-0.702762\pi\)
0.147859 + 0.989008i \(0.452762\pi\)
\(614\) −184.210 + 46.5899i −0.300016 + 0.0758793i
\(615\) −242.630 242.630i −0.394520 0.394520i
\(616\) 518.728 + 21.9193i 0.842091 + 0.0355832i
\(617\) 232.825 + 232.825i 0.377350 + 0.377350i 0.870145 0.492795i \(-0.164025\pi\)
−0.492795 + 0.870145i \(0.664025\pi\)
\(618\) 121.761 204.203i 0.197025 0.330426i
\(619\) 265.628 110.027i 0.429125 0.177749i −0.157658 0.987494i \(-0.550394\pi\)
0.586783 + 0.809745i \(0.300394\pi\)
\(620\) −253.895 + 26.1788i −0.409508 + 0.0422239i
\(621\) 58.9056 + 24.3995i 0.0948560 + 0.0392906i
\(622\) −498.110 72.7245i −0.800820 0.116920i
\(623\) −74.1840 −0.119076
\(624\) 9.17399 + 44.0139i 0.0147019 + 0.0705351i
\(625\) 148.435i 0.237496i
\(626\) −959.493 140.087i −1.53274 0.223781i
\(627\) 18.7318 45.2225i 0.0298752 0.0721252i
\(628\) −273.116 222.059i −0.434898 0.353597i
\(629\) 247.405 + 597.288i 0.393330 + 0.949583i
\(630\) 44.7645 75.0736i 0.0710547 0.119164i
\(631\) 728.483 728.483i 1.15449 1.15449i 0.168847 0.985642i \(-0.445996\pi\)
0.985642 0.168847i \(-0.0540044\pi\)
\(632\) −561.516 + 205.267i −0.888474 + 0.324790i
\(633\) 27.3577 27.3577i 0.0432192 0.0432192i
\(634\) −204.190 + 51.6433i −0.322067 + 0.0814563i
\(635\) 194.317 + 469.122i 0.306011 + 0.738775i
\(636\) 13.2323 + 3.94801i 0.0208055 + 0.00620756i
\(637\) −11.6241 + 28.0630i −0.0182482 + 0.0440550i
\(638\) 668.090 497.860i 1.04716 0.780345i
\(639\) 389.118i 0.608949i
\(640\) −334.374 + 55.0805i −0.522459 + 0.0860633i
\(641\) −253.220 −0.395038 −0.197519 0.980299i \(-0.563288\pi\)
−0.197519 + 0.980299i \(0.563288\pi\)
\(642\) 256.884 + 344.718i 0.400130 + 0.536944i
\(643\) 309.728 + 128.294i 0.481693 + 0.199524i 0.610297 0.792172i \(-0.291050\pi\)
−0.128605 + 0.991696i \(0.541050\pi\)
\(644\) −77.2149 + 258.796i −0.119899 + 0.401857i
\(645\) 298.632 123.697i 0.462995 0.191779i
\(646\) 12.3971 + 49.0165i 0.0191906 + 0.0758769i
\(647\) −59.9717 59.9717i −0.0926920 0.0926920i 0.659240 0.751932i \(-0.270878\pi\)
−0.751932 + 0.659240i \(0.770878\pi\)
\(648\) 24.7203 + 67.6233i 0.0381486 + 0.104357i
\(649\) −419.060 419.060i −0.645701 0.645701i
\(650\) −50.1379 29.8959i −0.0771352 0.0459938i
\(651\) −212.220 + 87.9045i −0.325991 + 0.135030i
\(652\) 238.013 292.738i 0.365050 0.448985i
\(653\) −427.960 177.267i −0.655375 0.271465i 0.0301159 0.999546i \(-0.490412\pi\)
−0.685491 + 0.728081i \(0.740412\pi\)
\(654\) 21.4134 146.667i 0.0327423 0.224261i
\(655\) 274.500 0.419084
\(656\) 244.296 + 1172.06i 0.372403 + 1.78667i
\(657\) 287.119i 0.437016i
\(658\) −71.6627 + 490.837i −0.108910 + 0.745953i
\(659\) −252.986 + 610.763i −0.383894 + 0.926802i 0.607311 + 0.794465i \(0.292248\pi\)
−0.991205 + 0.132338i \(0.957752\pi\)
\(660\) 22.1890 + 215.199i 0.0336197 + 0.326060i
\(661\) 63.1091 + 152.359i 0.0954753 + 0.230498i 0.964401 0.264445i \(-0.0851889\pi\)
−0.868925 + 0.494943i \(0.835189\pi\)
\(662\) −1032.10 615.414i −1.55906 0.929629i
\(663\) −20.9637 + 20.9637i −0.0316194 + 0.0316194i
\(664\) −29.8751 + 707.007i −0.0449927 + 1.06477i
\(665\) 24.6817 24.6817i 0.0371154 0.0371154i
\(666\) 90.1479 + 356.432i 0.135357 + 0.535183i
\(667\) 165.857 + 400.414i 0.248661 + 0.600320i
\(668\) −486.015 + 262.644i −0.727567 + 0.393179i
\(669\) −58.4518 + 141.115i −0.0873718 + 0.210934i
\(670\) −361.020 484.462i −0.538836 0.723077i
\(671\) 385.557i 0.574600i
\(672\) −274.188 + 133.536i −0.408018 + 0.198715i
\(673\) −243.863 −0.362352 −0.181176 0.983451i \(-0.557990\pi\)
−0.181176 + 0.983451i \(0.557990\pi\)
\(674\) 981.007 731.046i 1.45550 1.08464i
\(675\) −86.3667 35.7743i −0.127951 0.0529989i
\(676\) 585.454 316.381i 0.866056 0.468019i
\(677\) 160.394 66.4373i 0.236918 0.0981348i −0.261066 0.965321i \(-0.584074\pi\)
0.497984 + 0.867186i \(0.334074\pi\)
\(678\) −261.082 + 66.0321i −0.385077 + 0.0973925i
\(679\) 359.548 + 359.548i 0.529525 + 0.529525i
\(680\) −151.200 164.542i −0.222353 0.241973i
\(681\) 263.588 + 263.588i 0.387060 + 0.387060i
\(682\) 291.175 488.324i 0.426943 0.716018i
\(683\) 59.5121 24.6507i 0.0871334 0.0360918i −0.338691 0.940898i \(-0.609984\pi\)
0.425824 + 0.904806i \(0.359984\pi\)
\(684\) 2.94903 + 28.6011i 0.00431145 + 0.0418145i
\(685\) 193.665 + 80.2187i 0.282723 + 0.117108i
\(686\) −737.467 107.671i −1.07502 0.156955i
\(687\) −567.317 −0.825789
\(688\) −1108.13 209.907i −1.61065 0.305097i
\(689\) 3.23352i 0.00469307i
\(690\) −111.354 16.2578i −0.161383 0.0235620i
\(691\) 336.111 811.444i 0.486412 1.17430i −0.470100 0.882613i \(-0.655782\pi\)
0.956513 0.291691i \(-0.0942177\pi\)
\(692\) −652.372 + 802.369i −0.942734 + 1.15949i
\(693\) 74.5072 + 179.876i 0.107514 + 0.259562i
\(694\) 326.783 548.041i 0.470869 0.789684i
\(695\) 32.5558 32.5558i 0.0468428 0.0468428i
\(696\) −206.217 + 443.858i −0.296289 + 0.637727i
\(697\) −558.247 + 558.247i −0.800928 + 0.800928i
\(698\) −1323.26 + 334.676i −1.89579 + 0.479478i
\(699\) −59.3808 143.358i −0.0849510 0.205090i
\(700\) 113.212 379.444i 0.161731 0.542063i
\(701\) −472.080 + 1139.70i −0.673438 + 1.62582i 0.102290 + 0.994755i \(0.467383\pi\)
−0.775728 + 0.631068i \(0.782617\pi\)
\(702\) −13.5190 + 10.0744i −0.0192579 + 0.0143510i
\(703\) 146.821i 0.208849i
\(704\) 346.672 670.536i 0.492431 0.952465i
\(705\) −206.694 −0.293183
\(706\) −158.159 212.237i −0.224021 0.300619i
\(707\) 831.522 + 344.428i 1.17613 + 0.487168i
\(708\) 333.590 + 99.5305i 0.471172 + 0.140580i
\(709\) 210.722 87.2841i 0.297211 0.123109i −0.229095 0.973404i \(-0.573577\pi\)
0.526306 + 0.850295i \(0.323577\pi\)
\(710\) 168.400 + 665.828i 0.237182 + 0.937786i
\(711\) −158.531 158.531i −0.222969 0.222969i
\(712\) −45.4447 + 97.8145i −0.0638269 + 0.137380i
\(713\) 209.121 + 209.121i 0.293298 + 0.293298i
\(714\) −172.730 102.995i −0.241919 0.144250i
\(715\) −46.8033 + 19.3865i −0.0654591 + 0.0271140i
\(716\) −423.693 344.487i −0.591750 0.481127i
\(717\) 208.407 + 86.3252i 0.290666 + 0.120398i
\(718\) −99.7936 + 683.514i −0.138988 + 0.951969i
\(719\) −9.71810 −0.0135161 −0.00675807 0.999977i \(-0.502151\pi\)
−0.00675807 + 0.999977i \(0.502151\pi\)
\(720\) −71.5649 105.013i −0.0993957 0.145852i
\(721\) 377.647i 0.523782i
\(722\) 102.648 703.064i 0.142172 0.973773i
\(723\) −204.115 + 492.777i −0.282316 + 0.681572i
\(724\) 1169.59 120.595i 1.61546 0.166568i
\(725\) −243.177 587.082i −0.335417 0.809768i
\(726\) −53.8863 32.1310i −0.0742236 0.0442576i
\(727\) 300.549 300.549i 0.413410 0.413410i −0.469514 0.882925i \(-0.655571\pi\)
0.882925 + 0.469514i \(0.155571\pi\)
\(728\) −48.3212 52.5850i −0.0663752 0.0722322i
\(729\) −19.0919 + 19.0919i −0.0261891 + 0.0261891i
\(730\) 124.257 + 491.296i 0.170215 + 0.673008i
\(731\) −284.605 687.097i −0.389336 0.939941i
\(732\) −107.673 199.247i −0.147095 0.272195i
\(733\) 242.627 585.754i 0.331006 0.799119i −0.667507 0.744604i \(-0.732639\pi\)
0.998513 0.0545157i \(-0.0173615\pi\)
\(734\) 535.395 + 718.458i 0.729420 + 0.978826i
\(735\) 85.8563i 0.116811i
\(736\) 293.931 + 260.348i 0.399363 + 0.353733i
\(737\) 1345.81 1.82607
\(738\) −360.001 + 268.273i −0.487807 + 0.363513i
\(739\) 13.6426 + 5.65097i 0.0184610 + 0.00764678i 0.391895 0.920010i \(-0.371820\pi\)
−0.373434 + 0.927657i \(0.621820\pi\)
\(740\) −308.508 570.885i −0.416902 0.771466i
\(741\) −6.22039 + 2.57657i −0.00839459 + 0.00347715i
\(742\) −21.2645 + 5.37816i −0.0286583 + 0.00724819i
\(743\) 819.079 + 819.079i 1.10239 + 1.10239i 0.994121 + 0.108273i \(0.0345320\pi\)
0.108273 + 0.994121i \(0.465468\pi\)
\(744\) −14.0995 + 333.670i −0.0189509 + 0.448481i
\(745\) 1.15529 + 1.15529i 0.00155072 + 0.00155072i
\(746\) 510.533 856.205i 0.684361 1.14773i
\(747\) −245.165 + 101.550i −0.328199 + 0.135944i
\(748\) 495.134 51.0528i 0.661944 0.0682524i
\(749\) −630.892 261.324i −0.842313 0.348897i
\(750\) 390.141 + 56.9609i 0.520188 + 0.0759479i
\(751\) 1444.77 1.92380 0.961900 0.273400i \(-0.0881482\pi\)
0.961900 + 0.273400i \(0.0881482\pi\)
\(752\) 603.288 + 395.174i 0.802244 + 0.525498i
\(753\) 368.807i 0.489783i
\(754\) −113.404 16.5571i −0.150403 0.0219590i
\(755\) 224.355 541.642i 0.297159 0.717406i
\(756\) −88.7371 72.1484i −0.117377 0.0954344i
\(757\) 89.2346 + 215.431i 0.117879 + 0.284586i 0.971796 0.235825i \(-0.0757791\pi\)
−0.853916 + 0.520410i \(0.825779\pi\)
\(758\) 283.226 474.993i 0.373649 0.626640i
\(759\) 177.250 177.250i 0.233531 0.233531i
\(760\) −17.4239 47.6637i −0.0229262 0.0627154i
\(761\) 141.461 141.461i 0.185888 0.185888i −0.608028 0.793916i \(-0.708039\pi\)
0.793916 + 0.608028i \(0.208039\pi\)
\(762\) 644.111 162.907i 0.845291 0.213789i
\(763\) 90.0983 + 217.517i 0.118084 + 0.285081i
\(764\) 460.468 + 137.386i 0.602706 + 0.179825i
\(765\) 32.0683 77.4196i 0.0419193 0.101202i
\(766\) 41.8387 31.1782i 0.0546197 0.0407026i
\(767\) 81.5181i 0.106282i
\(768\) 8.10704 + 443.331i 0.0105560 + 0.577254i
\(769\) −380.236 −0.494455 −0.247227 0.968958i \(-0.579519\pi\)
−0.247227 + 0.968958i \(0.579519\pi\)
\(770\) −205.336 275.545i −0.266670 0.357851i
\(771\) −524.975 217.452i −0.680902 0.282039i
\(772\) −115.662 + 387.655i −0.149821 + 0.502144i
\(773\) 419.067 173.583i 0.542131 0.224558i −0.0947763 0.995499i \(-0.530214\pi\)
0.636907 + 0.770941i \(0.280214\pi\)
\(774\) −103.703 410.026i −0.133983 0.529749i
\(775\) −306.611 306.611i −0.395628 0.395628i
\(776\) 694.335 253.821i 0.894761 0.327088i
\(777\) −412.945 412.945i −0.531460 0.531460i
\(778\) 548.933 + 327.315i 0.705569 + 0.420713i
\(779\) −165.644 + 68.6121i −0.212637 + 0.0880771i
\(780\) 18.7728 23.0891i 0.0240677 0.0296014i
\(781\) −1413.37 585.438i −1.80970 0.749600i
\(782\) −37.4062 + 256.205i −0.0478340 + 0.327628i
\(783\) −183.534 −0.234398
\(784\) −164.147 + 250.593i −0.209371 + 0.319634i
\(785\) 232.978i 0.296788i
\(786\) 51.8886 355.399i 0.0660160 0.452162i
\(787\) 126.625 305.700i 0.160896 0.388436i −0.822787 0.568350i \(-0.807582\pi\)
0.983682 + 0.179914i \(0.0575819\pi\)
\(788\) 58.4786 + 567.153i 0.0742114 + 0.719738i
\(789\) 168.721 + 407.328i 0.213841 + 0.516258i
\(790\) 339.874 + 202.658i 0.430220 + 0.256529i
\(791\) 302.477 302.477i 0.382398 0.382398i
\(792\) 282.816 + 11.9506i 0.357092 + 0.0150892i
\(793\) 37.5004 37.5004i 0.0472893 0.0472893i
\(794\) −189.000 747.280i −0.238035 0.941159i
\(795\) −3.49759 8.44393i −0.00439948 0.0106213i
\(796\) 233.030 125.930i 0.292752 0.158204i
\(797\) 438.827 1059.42i 0.550598 1.32926i −0.366433 0.930445i \(-0.619421\pi\)
0.917031 0.398817i \(-0.130579\pi\)
\(798\) −27.2902 36.6214i −0.0341983 0.0458915i
\(799\) 475.565i 0.595200i
\(800\) −430.959 381.719i −0.538698 0.477149i
\(801\) −40.4460 −0.0504944
\(802\) −507.441 + 378.145i −0.632719 + 0.471502i
\(803\) −1042.89 431.978i −1.29874 0.537955i
\(804\) −695.484 + 375.841i −0.865029 + 0.467464i
\(805\) 165.146 68.4056i 0.205150 0.0849758i
\(806\) −75.8165 + 19.1753i −0.0940652 + 0.0237907i
\(807\) −295.470 295.470i −0.366134 0.366134i
\(808\) 963.527 885.400i 1.19248 1.09579i
\(809\) 626.958 + 626.958i 0.774979 + 0.774979i 0.978972 0.203993i \(-0.0653921\pi\)
−0.203993 + 0.978972i \(0.565392\pi\)
\(810\) 24.4061 40.9310i 0.0301310 0.0505320i
\(811\) −336.058 + 139.200i −0.414375 + 0.171640i −0.580124 0.814528i \(-0.696996\pi\)
0.165749 + 0.986168i \(0.446996\pi\)
\(812\) −79.7353 773.311i −0.0981962 0.952354i
\(813\) 414.475 + 171.681i 0.509809 + 0.211170i
\(814\) 1430.28 + 208.822i 1.75710 + 0.256538i
\(815\) −249.717 −0.306401
\(816\) −241.616 + 164.658i −0.296098 + 0.201786i
\(817\) 168.897i 0.206728i
\(818\) −296.353 43.2678i −0.362290 0.0528946i
\(819\) 10.2485 24.7421i 0.0125135 0.0302102i
\(820\) 499.905 614.846i 0.609640 0.749812i
\(821\) −501.999 1211.93i −0.611448 1.47617i −0.861410 0.507910i \(-0.830418\pi\)
0.249963 0.968256i \(-0.419582\pi\)
\(822\) 140.469 235.578i 0.170887 0.286591i
\(823\) 76.4524 76.4524i 0.0928948 0.0928948i −0.659132 0.752027i \(-0.729076\pi\)
0.752027 + 0.659132i \(0.229076\pi\)
\(824\) 497.942 + 231.344i 0.604298 + 0.280758i
\(825\) −259.882 + 259.882i −0.315008 + 0.315008i
\(826\) −536.084 + 135.585i −0.649012 + 0.164146i
\(827\) −539.074 1301.44i −0.651843 1.57369i −0.810101 0.586290i \(-0.800588\pi\)
0.158259 0.987398i \(-0.449412\pi\)
\(828\) −42.0984 + 141.099i −0.0508435 + 0.170409i
\(829\) −531.797 + 1283.87i −0.641492 + 1.54870i 0.183175 + 0.983080i \(0.441363\pi\)
−0.824667 + 0.565619i \(0.808637\pi\)
\(830\) 375.558 279.866i 0.452480 0.337187i
\(831\) 215.453i 0.259269i
\(832\) −98.9367 + 31.5000i −0.118914 + 0.0378606i
\(833\) −197.539 −0.237142
\(834\) −35.9964 48.3045i −0.0431612 0.0579190i
\(835\) 337.814 + 139.927i 0.404568 + 0.167578i
\(836\) 108.323 + 32.3195i 0.129573 + 0.0386596i
\(837\) −115.705 + 47.9265i −0.138238 + 0.0572599i
\(838\) 121.109 + 478.850i 0.144522 + 0.571420i
\(839\) −247.226 247.226i −0.294667 0.294667i 0.544253 0.838921i \(-0.316813\pi\)
−0.838921 + 0.544253i \(0.816813\pi\)
\(840\) 183.064 + 85.0516i 0.217933 + 0.101252i
\(841\) −287.496 287.496i −0.341850 0.341850i
\(842\) 511.034 + 304.716i 0.606928 + 0.361896i
\(843\) −622.830 + 257.985i −0.738825 + 0.306031i
\(844\) 69.3269 + 56.3667i 0.0821408 + 0.0667852i
\(845\) −406.931 168.557i −0.481576 0.199475i
\(846\) −39.0713 + 267.610i −0.0461836 + 0.316324i
\(847\) 99.6554 0.117657
\(848\) −5.93520 + 31.3327i −0.00699906 + 0.0369489i
\(849\) 400.284i 0.471477i
\(850\) 54.8445 375.645i 0.0645229 0.441935i
\(851\) −287.732 + 694.647i −0.338111 + 0.816272i
\(852\) 893.891 92.1682i 1.04917 0.108179i
\(853\) −589.484 1423.14i −0.691072 1.66839i −0.742610 0.669724i \(-0.766413\pi\)
0.0515387 0.998671i \(-0.483587\pi\)
\(854\) 308.985 + 184.240i 0.361809 + 0.215738i
\(855\) 13.4568 13.4568i 0.0157389 0.0157389i
\(856\) −731.047 + 671.770i −0.854027 + 0.784778i
\(857\) −379.015 + 379.015i −0.442258 + 0.442258i −0.892770 0.450512i \(-0.851241\pi\)
0.450512 + 0.892770i \(0.351241\pi\)
\(858\) 16.2529 + 64.2615i 0.0189427 + 0.0748969i
\(859\) −277.726 670.491i −0.323314 0.780548i −0.999057 0.0434113i \(-0.986177\pi\)
0.675744 0.737137i \(-0.263823\pi\)
\(860\) 354.895 + 656.724i 0.412669 + 0.763633i
\(861\) 272.910 658.863i 0.316969 0.765230i
\(862\) 105.731 + 141.883i 0.122658 + 0.164597i
\(863\) 885.356i 1.02591i 0.858417 + 0.512953i \(0.171448\pi\)
−0.858417 + 0.512953i \(0.828552\pi\)
\(864\) −149.490 + 72.8056i −0.173021 + 0.0842657i
\(865\) 684.452 0.791274
\(866\) −1014.20 + 755.778i −1.17113 + 0.872723i
\(867\) 284.331 + 117.774i 0.327948 + 0.135841i
\(868\) −252.203 466.695i −0.290557 0.537667i
\(869\) −814.338 + 337.310i −0.937097 + 0.388158i
\(870\) 314.049 79.4283i 0.360975 0.0912969i
\(871\) −130.898 130.898i −0.150284 0.150284i
\(872\) 341.998 + 14.4514i 0.392199 + 0.0165727i
\(873\) 196.030 + 196.030i 0.224547 + 0.224547i
\(874\) −30.1146 + 50.5045i −0.0344560 + 0.0577855i
\(875\) −578.606 + 239.666i −0.661264 + 0.273904i
\(876\) 659.577 68.0083i 0.752941 0.0776350i
\(877\) 451.165 + 186.879i 0.514441 + 0.213089i 0.624773 0.780806i \(-0.285191\pi\)
−0.110332 + 0.993895i \(0.535191\pi\)
\(878\) 963.034 + 140.604i 1.09685 + 0.160141i
\(879\) 380.750 0.433162
\(880\) −489.105 + 101.946i −0.555801 + 0.115848i
\(881\) 845.720i 0.959955i 0.877281 + 0.479978i \(0.159355\pi\)
−0.877281 + 0.479978i \(0.840645\pi\)
\(882\) −111.159 16.2294i −0.126031 0.0184007i
\(883\) −615.155 + 1485.12i −0.696665 + 1.68190i 0.0342344 + 0.999414i \(0.489101\pi\)
−0.730900 + 0.682485i \(0.760899\pi\)
\(884\) −53.1238 43.1927i −0.0600948 0.0488605i
\(885\) −88.1752 212.874i −0.0996330 0.240535i
\(886\) 45.0625 75.5733i 0.0508606 0.0852972i
\(887\) 889.029 889.029i 1.00229 1.00229i 0.00229019 0.999997i \(-0.499271\pi\)
0.999997 0.00229019i \(-0.000728990\pi\)
\(888\) −797.451 + 291.516i −0.898030 + 0.328283i
\(889\) −746.236 + 746.236i −0.839410 + 0.839410i
\(890\) 69.2080 17.5039i 0.0777617 0.0196673i
\(891\) 40.6222 + 98.0706i 0.0455917 + 0.110068i
\(892\) −338.018 100.852i −0.378944 0.113062i
\(893\) −41.3303 + 99.7802i −0.0462826 + 0.111736i
\(894\) 1.71416 1.27739i 0.00191740 0.00142885i
\(895\) 361.427i 0.403829i
\(896\) −371.708 598.240i −0.414853 0.667679i
\(897\) −34.4797 −0.0384389
\(898\) 851.720 + 1142.94i 0.948464 + 1.27276i
\(899\) −786.509 325.783i −0.874871 0.362383i
\(900\) 61.7242 206.877i 0.0685825 0.229863i
\(901\) −19.4279 + 8.04731i −0.0215626 + 0.00893153i
\(902\) 432.801 + 1711.24i 0.479824 + 1.89716i
\(903\) 475.035 + 475.035i 0.526064 + 0.526064i
\(904\) −213.531 584.122i −0.236207 0.646153i
\(905\) −550.290 550.290i −0.608055 0.608055i
\(906\) −658.862 392.863i −0.727221 0.433623i
\(907\) −221.733 + 91.8447i −0.244468 + 0.101262i −0.501553 0.865127i \(-0.667238\pi\)
0.257085 + 0.966389i \(0.417238\pi\)
\(908\) −543.086 + 667.955i −0.598112 + 0.735633i
\(909\) 453.355 + 187.786i 0.498741 + 0.206585i
\(910\) −6.82876 + 46.7720i −0.00750413 + 0.0513978i
\(911\) −434.295 −0.476723 −0.238361 0.971177i \(-0.576610\pi\)
−0.238361 + 0.971177i \(0.576610\pi\)
\(912\) −65.0046 + 13.5492i −0.0712769 + 0.0148565i
\(913\) 1043.28i 1.14270i
\(914\) −87.9784 + 602.588i −0.0962565 + 0.659287i
\(915\) −57.3646 + 138.490i −0.0626935 + 0.151356i
\(916\) −134.377 1303.25i −0.146700 1.42276i
\(917\) 218.324 + 527.081i 0.238085 + 0.574789i
\(918\) −94.1746 56.1539i −0.102587 0.0611698i
\(919\) 287.621 287.621i 0.312971 0.312971i −0.533088 0.846060i \(-0.678969\pi\)
0.846060 + 0.533088i \(0.178969\pi\)
\(920\) 10.9720 259.656i 0.0119260 0.282234i
\(921\) 116.357 116.357i 0.126338 0.126338i
\(922\) 253.022 + 1000.42i 0.274428 + 1.08505i
\(923\) 80.5274 + 194.410i 0.0872453 + 0.210629i
\(924\) −395.568 + 213.766i −0.428104 + 0.231348i
\(925\) 421.870 1018.48i 0.456075 1.10106i
\(926\) 441.085 + 591.903i 0.476334 + 0.639204i
\(927\) 205.897i 0.222111i
\(928\) −1068.49 368.592i −1.15139 0.397190i
\(929\) 1213.34 1.30608 0.653038 0.757325i \(-0.273494\pi\)
0.653038 + 0.757325i \(0.273494\pi\)
\(930\) 177.244 132.082i 0.190585 0.142024i
\(931\) −41.4466 17.1677i −0.0445183 0.0184401i
\(932\) 315.260 170.367i 0.338261 0.182797i
\(933\) 402.764 166.831i 0.431688 0.178811i
\(934\) −1351.81 + 341.896i −1.44733 + 0.366055i
\(935\) −232.959 232.959i −0.249155 0.249155i
\(936\) −26.3452 28.6699i −0.0281466 0.0306303i
\(937\) −806.355 806.355i −0.860571 0.860571i 0.130833 0.991404i \(-0.458235\pi\)
−0.991404 + 0.130833i \(0.958235\pi\)
\(938\) 643.101 1078.53i 0.685609 1.14982i
\(939\) 775.833 321.360i 0.826233 0.342237i
\(940\) −48.9584 474.822i −0.0520834 0.505130i
\(941\) 715.079 + 296.195i 0.759914 + 0.314767i 0.728779 0.684749i \(-0.240088\pi\)
0.0311346 + 0.999515i \(0.490088\pi\)
\(942\) 301.641 + 44.0398i 0.320213 + 0.0467514i
\(943\) −918.168 −0.973667
\(944\) −149.628 + 789.905i −0.158504 + 0.836764i
\(945\) 75.6963i 0.0801019i
\(946\) −1645.34 240.221i −1.73926 0.253933i
\(947\) 93.1503 224.885i 0.0983636 0.237471i −0.867036 0.498245i \(-0.833978\pi\)
0.965400 + 0.260775i \(0.0839779\pi\)
\(948\) 326.631 401.732i 0.344547 0.423767i
\(949\) 59.4189 + 143.450i 0.0626121 + 0.151159i
\(950\) 44.1536 74.0492i 0.0464775 0.0779465i
\(951\) 128.978 128.978i 0.135623 0.135623i
\(952\) 195.688 421.196i 0.205555 0.442433i
\(953\) 186.819 186.819i 0.196032 0.196032i −0.602264 0.798297i \(-0.705735\pi\)
0.798297 + 0.602264i \(0.205735\pi\)
\(954\) −11.5936 + 2.93223i −0.0121527 + 0.00307362i
\(955\) −121.712 293.838i −0.127447 0.307684i
\(956\) −148.944 + 499.205i −0.155799 + 0.522181i
\(957\) −276.131 + 666.640i −0.288538 + 0.696593i
\(958\) −606.220 + 451.755i −0.632798 + 0.471561i
\(959\) 435.669i 0.454295i
\(960\) 224.288 189.274i 0.233633 0.197161i
\(961\) 380.091 0.395516
\(962\) −118.803 159.424i −0.123495 0.165721i
\(963\) −343.969 142.477i −0.357185 0.147951i
\(964\) −1180.36 352.176i −1.22444 0.365328i
\(965\) 247.375 102.466i 0.256347 0.106182i
\(966\) −57.3483 226.747i −0.0593668 0.234728i
\(967\) 273.953 + 273.953i 0.283302 + 0.283302i 0.834425 0.551122i \(-0.185800\pi\)
−0.551122 + 0.834425i \(0.685800\pi\)
\(968\) 61.0484 131.400i 0.0630665 0.135743i
\(969\) −30.9615 30.9615i −0.0319520 0.0319520i
\(970\) −420.266 250.594i −0.433264 0.258344i
\(971\) −897.858 + 371.905i −0.924673 + 0.383012i −0.793655 0.608368i \(-0.791825\pi\)
−0.131018 + 0.991380i \(0.541825\pi\)
\(972\) −48.3805 39.3361i −0.0497742 0.0404692i
\(973\) 88.4053 + 36.6187i 0.0908585 + 0.0376348i
\(974\) −90.8997 + 622.597i −0.0933261 + 0.639216i
\(975\) 50.5538 0.0518500
\(976\) 432.210 294.544i 0.442838 0.301787i
\(977\) 945.557i 0.967816i 0.875119 + 0.483908i \(0.160783\pi\)
−0.875119 + 0.483908i \(0.839217\pi\)
\(978\) −47.2039 + 323.313i −0.0482658 + 0.330586i
\(979\) −60.8520 + 146.910i −0.0621573 + 0.150061i
\(980\) 197.231 20.3363i 0.201256 0.0207513i
\(981\) 49.1226 + 118.592i 0.0500740 + 0.120889i
\(982\) −43.6077 26.0021i −0.0444070 0.0264788i
\(983\) −724.186 + 724.186i −0.736710 + 0.736710i −0.971940 0.235230i \(-0.924416\pi\)
0.235230 + 0.971940i \(0.424416\pi\)
\(984\) −701.553 763.459i −0.712961 0.775873i
\(985\) 266.844 266.844i 0.270908 0.270908i
\(986\) −182.750 722.568i −0.185345 0.732827i
\(987\) −164.395 396.884i −0.166560 0.402111i
\(988\) −7.39234 13.6793i −0.00748213 0.0138455i
\(989\) 330.996 799.095i 0.334678 0.807983i
\(990\) −111.952 150.230i −0.113082 0.151748i
\(991\) 786.054i 0.793192i −0.917993 0.396596i \(-0.870191\pi\)
0.917993 0.396596i \(-0.129809\pi\)
\(992\) −769.854 + 46.6449i −0.776063 + 0.0470211i
\(993\) 1040.66 1.04800
\(994\) −1144.55 + 852.921i −1.15146 + 0.858070i
\(995\) −161.972 67.0912i −0.162786 0.0674283i
\(996\) −291.355 539.144i −0.292525 0.541309i
\(997\) 389.243 161.230i 0.390414 0.161715i −0.178837 0.983879i \(-0.557233\pi\)
0.569251 + 0.822164i \(0.307233\pi\)
\(998\) 846.407 214.071i 0.848103 0.214500i
\(999\) −225.142 225.142i −0.225367 0.225367i
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 96.3.m.a.19.6 64
3.2 odd 2 288.3.u.b.19.11 64
4.3 odd 2 384.3.m.a.367.6 64
32.5 even 8 384.3.m.a.271.6 64
32.27 odd 8 inner 96.3.m.a.91.6 yes 64
96.59 even 8 288.3.u.b.91.11 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.3.m.a.19.6 64 1.1 even 1 trivial
96.3.m.a.91.6 yes 64 32.27 odd 8 inner
288.3.u.b.19.11 64 3.2 odd 2
288.3.u.b.91.11 64 96.59 even 8
384.3.m.a.271.6 64 32.5 even 8
384.3.m.a.367.6 64 4.3 odd 2