Properties

Label 429.2.bd.b.175.5
Level $429$
Weight $2$
Character 429.175
Analytic conductor $3.426$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(76,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bd (of order \(12\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 175.5
Character \(\chi\) \(=\) 429.175
Dual form 429.2.bd.b.76.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.19562 + 0.320366i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.405173 + 0.233927i) q^{4} +(-2.87074 + 2.87074i) q^{5} +(-0.320366 + 1.19562i) q^{6} +(2.15836 + 0.578331i) q^{7} +(2.16000 - 2.16000i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.19562 + 0.320366i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.405173 + 0.233927i) q^{4} +(-2.87074 + 2.87074i) q^{5} +(-0.320366 + 1.19562i) q^{6} +(2.15836 + 0.578331i) q^{7} +(2.16000 - 2.16000i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.51263 - 4.35201i) q^{10} +(-3.00135 - 1.41135i) q^{11} +0.467854i q^{12} +(-1.22385 + 3.39149i) q^{13} -2.76586 q^{14} +(1.05076 + 3.92150i) q^{15} +(-1.42270 + 2.46419i) q^{16} +(-1.96225 - 3.39871i) q^{17} +(0.875256 + 0.875256i) q^{18} +(0.872934 - 3.25783i) q^{19} +(0.491604 - 1.83469i) q^{20} +(1.58003 - 1.58003i) q^{21} +(4.04063 + 0.725915i) q^{22} +(-2.83426 - 1.63636i) q^{23} +(-0.790616 - 2.95062i) q^{24} -11.4823i q^{25} +(0.376748 - 4.44702i) q^{26} -1.00000 q^{27} +(-1.00980 + 0.270575i) q^{28} +(-3.17928 - 1.83556i) q^{29} +(-2.51263 - 4.35201i) q^{30} +(1.66735 - 1.66735i) q^{31} +(-0.669662 + 2.49921i) q^{32} +(-2.72294 + 1.89357i) q^{33} +(3.43494 + 3.43494i) q^{34} +(-7.85633 + 4.53586i) q^{35} +(0.405173 + 0.233927i) q^{36} +(-8.67054 + 2.32326i) q^{37} +4.17480i q^{38} +(2.32519 + 2.75563i) q^{39} +12.4016i q^{40} +(-2.09872 + 0.562351i) q^{41} +(-1.38293 + 2.39531i) q^{42} +(-5.45123 - 9.44180i) q^{43} +(1.54622 - 0.130253i) q^{44} +(3.92150 + 1.05076i) q^{45} +(3.91294 + 1.04847i) q^{46} +(3.31640 + 3.31640i) q^{47} +(1.42270 + 2.46419i) q^{48} +(-1.73812 - 1.00350i) q^{49} +(3.67853 + 13.7285i) q^{50} -3.92449 q^{51} +(-0.297488 - 1.66043i) q^{52} -5.39540 q^{53} +(1.19562 - 0.320366i) q^{54} +(12.6677 - 4.56446i) q^{55} +(5.91127 - 3.41287i) q^{56} +(-2.38490 - 2.38490i) q^{57} +(4.38927 + 1.17610i) q^{58} +(-0.0211155 + 0.0788041i) q^{59} +(-1.34309 - 1.34309i) q^{60} +(-2.06440 + 1.19188i) q^{61} +(-1.45936 + 2.52769i) q^{62} +(-0.578331 - 2.15836i) q^{63} -8.89346i q^{64} +(-6.22271 - 13.2494i) q^{65} +(2.64897 - 3.13633i) q^{66} +(2.69165 + 10.0454i) q^{67} +(1.59010 + 0.918045i) q^{68} +(-2.83426 + 1.63636i) q^{69} +(7.94007 - 7.94007i) q^{70} +(11.1860 + 2.99729i) q^{71} +(-2.95062 - 0.790616i) q^{72} +(10.1099 - 10.1099i) q^{73} +(9.62240 - 5.55549i) q^{74} +(-9.94395 - 5.74114i) q^{75} +(0.408406 + 1.52419i) q^{76} +(-5.66176 - 4.78198i) q^{77} +(-3.66286 - 2.54978i) q^{78} +9.18864i q^{79} +(-2.98985 - 11.1583i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.32912 - 1.34472i) q^{82} +(4.52047 + 4.52047i) q^{83} +(-0.270575 + 1.00980i) q^{84} +(15.3899 + 4.12371i) q^{85} +(9.54243 + 9.54243i) q^{86} +(-3.17928 + 1.83556i) q^{87} +(-9.53145 + 3.43439i) q^{88} +(-15.8394 + 4.24415i) q^{89} -5.02526 q^{90} +(-4.60292 + 6.61226i) q^{91} +1.53116 q^{92} +(-0.610293 - 2.27765i) q^{93} +(-5.02762 - 2.90270i) q^{94} +(6.84643 + 11.8584i) q^{95} +(1.82955 + 1.82955i) q^{96} +(-4.63608 - 1.24223i) q^{97} +(2.39962 + 0.642977i) q^{98} +(0.278406 + 3.30492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19562 + 0.320366i −0.845432 + 0.226533i −0.655435 0.755252i \(-0.727515\pi\)
−0.189997 + 0.981785i \(0.560848\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.405173 + 0.233927i −0.202587 + 0.116964i
\(5\) −2.87074 + 2.87074i −1.28383 + 1.28383i −0.345365 + 0.938468i \(0.612245\pi\)
−0.938468 + 0.345365i \(0.887755\pi\)
\(6\) −0.320366 + 1.19562i −0.130789 + 0.488111i
\(7\) 2.15836 + 0.578331i 0.815784 + 0.218589i 0.642502 0.766284i \(-0.277896\pi\)
0.173282 + 0.984872i \(0.444563\pi\)
\(8\) 2.16000 2.16000i 0.763677 0.763677i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 2.51263 4.35201i 0.794564 1.37622i
\(11\) −3.00135 1.41135i −0.904940 0.425539i
\(12\) 0.467854i 0.135058i
\(13\) −1.22385 + 3.39149i −0.339436 + 0.940629i
\(14\) −2.76586 −0.739208
\(15\) 1.05076 + 3.92150i 0.271306 + 1.01253i
\(16\) −1.42270 + 2.46419i −0.355676 + 0.616048i
\(17\) −1.96225 3.39871i −0.475915 0.824309i 0.523705 0.851900i \(-0.324550\pi\)
−0.999619 + 0.0275914i \(0.991216\pi\)
\(18\) 0.875256 + 0.875256i 0.206300 + 0.206300i
\(19\) 0.872934 3.25783i 0.200265 0.747398i −0.790576 0.612364i \(-0.790219\pi\)
0.990841 0.135035i \(-0.0431145\pi\)
\(20\) 0.491604 1.83469i 0.109926 0.410249i
\(21\) 1.58003 1.58003i 0.344791 0.344791i
\(22\) 4.04063 + 0.725915i 0.861464 + 0.154766i
\(23\) −2.83426 1.63636i −0.590984 0.341205i 0.174503 0.984657i \(-0.444168\pi\)
−0.765486 + 0.643452i \(0.777502\pi\)
\(24\) −0.790616 2.95062i −0.161384 0.602293i
\(25\) 11.4823i 2.29646i
\(26\) 0.376748 4.44702i 0.0738864 0.872132i
\(27\) −1.00000 −0.192450
\(28\) −1.00980 + 0.270575i −0.190834 + 0.0511338i
\(29\) −3.17928 1.83556i −0.590378 0.340855i 0.174869 0.984592i \(-0.444050\pi\)
−0.765247 + 0.643737i \(0.777383\pi\)
\(30\) −2.51263 4.35201i −0.458742 0.794564i
\(31\) 1.66735 1.66735i 0.299465 0.299465i −0.541339 0.840804i \(-0.682082\pi\)
0.840804 + 0.541339i \(0.182082\pi\)
\(32\) −0.669662 + 2.49921i −0.118381 + 0.441803i
\(33\) −2.72294 + 1.89357i −0.474003 + 0.329628i
\(34\) 3.43494 + 3.43494i 0.589087 + 0.589087i
\(35\) −7.85633 + 4.53586i −1.32796 + 0.766700i
\(36\) 0.405173 + 0.233927i 0.0675289 + 0.0389878i
\(37\) −8.67054 + 2.32326i −1.42543 + 0.381942i −0.887406 0.460988i \(-0.847495\pi\)
−0.538022 + 0.842931i \(0.680828\pi\)
\(38\) 4.17480i 0.677241i
\(39\) 2.32519 + 2.75563i 0.372328 + 0.441254i
\(40\) 12.4016i 1.96087i
\(41\) −2.09872 + 0.562351i −0.327765 + 0.0878244i −0.418949 0.908010i \(-0.637602\pi\)
0.0911841 + 0.995834i \(0.470935\pi\)
\(42\) −1.38293 + 2.39531i −0.213391 + 0.369604i
\(43\) −5.45123 9.44180i −0.831304 1.43986i −0.897004 0.442021i \(-0.854262\pi\)
0.0657005 0.997839i \(-0.479072\pi\)
\(44\) 1.54622 0.130253i 0.233101 0.0196364i
\(45\) 3.92150 + 1.05076i 0.584583 + 0.156639i
\(46\) 3.91294 + 1.04847i 0.576931 + 0.154588i
\(47\) 3.31640 + 3.31640i 0.483746 + 0.483746i 0.906326 0.422579i \(-0.138875\pi\)
−0.422579 + 0.906326i \(0.638875\pi\)
\(48\) 1.42270 + 2.46419i 0.205349 + 0.355676i
\(49\) −1.73812 1.00350i −0.248303 0.143358i
\(50\) 3.67853 + 13.7285i 0.520223 + 1.94150i
\(51\) −3.92449 −0.549539
\(52\) −0.297488 1.66043i −0.0412541 0.230261i
\(53\) −5.39540 −0.741115 −0.370557 0.928810i \(-0.620833\pi\)
−0.370557 + 0.928810i \(0.620833\pi\)
\(54\) 1.19562 0.320366i 0.162704 0.0435963i
\(55\) 12.6677 4.56446i 1.70811 0.615471i
\(56\) 5.91127 3.41287i 0.789926 0.456064i
\(57\) −2.38490 2.38490i −0.315888 0.315888i
\(58\) 4.38927 + 1.17610i 0.576340 + 0.154430i
\(59\) −0.0211155 + 0.0788041i −0.00274900 + 0.0102594i −0.967287 0.253686i \(-0.918357\pi\)
0.964538 + 0.263945i \(0.0850238\pi\)
\(60\) −1.34309 1.34309i −0.173392 0.173392i
\(61\) −2.06440 + 1.19188i −0.264320 + 0.152605i −0.626303 0.779579i \(-0.715433\pi\)
0.361984 + 0.932184i \(0.382100\pi\)
\(62\) −1.45936 + 2.52769i −0.185339 + 0.321016i
\(63\) −0.578331 2.15836i −0.0728629 0.271928i
\(64\) 8.89346i 1.11168i
\(65\) −6.22271 13.2494i −0.771833 1.64339i
\(66\) 2.64897 3.13633i 0.326066 0.386055i
\(67\) 2.69165 + 10.0454i 0.328837 + 1.22724i 0.910398 + 0.413734i \(0.135776\pi\)
−0.581561 + 0.813503i \(0.697558\pi\)
\(68\) 1.59010 + 0.918045i 0.192828 + 0.111329i
\(69\) −2.83426 + 1.63636i −0.341205 + 0.196995i
\(70\) 7.94007 7.94007i 0.949020 0.949020i
\(71\) 11.1860 + 2.99729i 1.32754 + 0.355713i 0.851797 0.523871i \(-0.175513\pi\)
0.475742 + 0.879585i \(0.342179\pi\)
\(72\) −2.95062 0.790616i −0.347734 0.0931750i
\(73\) 10.1099 10.1099i 1.18327 1.18327i 0.204383 0.978891i \(-0.434481\pi\)
0.978891 0.204383i \(-0.0655187\pi\)
\(74\) 9.62240 5.55549i 1.11858 0.645813i
\(75\) −9.94395 5.74114i −1.14823 0.662930i
\(76\) 0.408406 + 1.52419i 0.0468473 + 0.174837i
\(77\) −5.66176 4.78198i −0.645218 0.544958i
\(78\) −3.66286 2.54978i −0.414737 0.288706i
\(79\) 9.18864i 1.03380i 0.856045 + 0.516902i \(0.172915\pi\)
−0.856045 + 0.516902i \(0.827085\pi\)
\(80\) −2.98985 11.1583i −0.334275 1.24753i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.32912 1.34472i 0.257208 0.148499i
\(83\) 4.52047 + 4.52047i 0.496186 + 0.496186i 0.910249 0.414062i \(-0.135890\pi\)
−0.414062 + 0.910249i \(0.635890\pi\)
\(84\) −0.270575 + 1.00980i −0.0295221 + 0.110178i
\(85\) 15.3899 + 4.12371i 1.66927 + 0.447280i
\(86\) 9.54243 + 9.54243i 1.02899 + 1.02899i
\(87\) −3.17928 + 1.83556i −0.340855 + 0.196793i
\(88\) −9.53145 + 3.43439i −1.01606 + 0.366108i
\(89\) −15.8394 + 4.24415i −1.67897 + 0.449879i −0.967507 0.252845i \(-0.918634\pi\)
−0.711463 + 0.702724i \(0.751967\pi\)
\(90\) −5.02526 −0.529709
\(91\) −4.60292 + 6.61226i −0.482517 + 0.693154i
\(92\) 1.53116 0.159634
\(93\) −0.610293 2.27765i −0.0632845 0.236181i
\(94\) −5.02762 2.90270i −0.518559 0.299390i
\(95\) 6.84643 + 11.8584i 0.702428 + 1.21664i
\(96\) 1.82955 + 1.82955i 0.186728 + 0.186728i
\(97\) −4.63608 1.24223i −0.470722 0.126130i 0.0156570 0.999877i \(-0.495016\pi\)
−0.486379 + 0.873748i \(0.661683\pi\)
\(98\) 2.39962 + 0.642977i 0.242398 + 0.0649504i
\(99\) 0.278406 + 3.30492i 0.0279808 + 0.332157i
\(100\) 2.68602 + 4.65232i 0.268602 + 0.465232i
\(101\) 5.99600 10.3854i 0.596624 1.03338i −0.396692 0.917952i \(-0.629842\pi\)
0.993316 0.115431i \(-0.0368249\pi\)
\(102\) 4.69221 1.25727i 0.464598 0.124489i
\(103\) 3.25244i 0.320472i −0.987079 0.160236i \(-0.948774\pi\)
0.987079 0.160236i \(-0.0512255\pi\)
\(104\) 4.68210 + 9.96915i 0.459118 + 0.977556i
\(105\) 9.07171i 0.885308i
\(106\) 6.45086 1.72850i 0.626562 0.167887i
\(107\) −5.55588 3.20769i −0.537107 0.310099i 0.206799 0.978383i \(-0.433695\pi\)
−0.743906 + 0.668285i \(0.767029\pi\)
\(108\) 0.405173 0.233927i 0.0389878 0.0225096i
\(109\) −0.738065 0.738065i −0.0706939 0.0706939i 0.670876 0.741570i \(-0.265918\pi\)
−0.741570 + 0.670876i \(0.765918\pi\)
\(110\) −13.6835 + 9.51567i −1.30467 + 0.907283i
\(111\) −2.32326 + 8.67054i −0.220515 + 0.822971i
\(112\) −4.49583 + 4.49583i −0.424816 + 0.424816i
\(113\) 6.58657 + 11.4083i 0.619613 + 1.07320i 0.989556 + 0.144146i \(0.0460436\pi\)
−0.369944 + 0.929054i \(0.620623\pi\)
\(114\) 3.61548 + 2.08740i 0.338621 + 0.195503i
\(115\) 12.8340 3.43886i 1.19678 0.320675i
\(116\) 1.71755 0.159470
\(117\) 3.54904 0.635856i 0.328109 0.0587849i
\(118\) 0.100985i 0.00929638i
\(119\) −2.26966 8.47048i −0.208059 0.776487i
\(120\) 10.7401 + 6.20081i 0.980434 + 0.566054i
\(121\) 7.01617 + 8.47192i 0.637833 + 0.770175i
\(122\) 2.08641 2.08641i 0.188894 0.188894i
\(123\) −0.562351 + 2.09872i −0.0507055 + 0.189235i
\(124\) −0.285528 + 1.06561i −0.0256412 + 0.0956942i
\(125\) 18.6089 + 18.6089i 1.66444 + 1.66444i
\(126\) 1.38293 + 2.39531i 0.123201 + 0.213391i
\(127\) −1.66088 + 2.87672i −0.147379 + 0.255268i −0.930258 0.366906i \(-0.880417\pi\)
0.782879 + 0.622174i \(0.213750\pi\)
\(128\) 1.50984 + 5.63479i 0.133452 + 0.498050i
\(129\) −10.9025 −0.959907
\(130\) 11.6847 + 13.8478i 1.02481 + 1.21453i
\(131\) 12.9015i 1.12721i −0.826046 0.563603i \(-0.809415\pi\)
0.826046 0.563603i \(-0.190585\pi\)
\(132\) 0.660307 1.40419i 0.0574724 0.122219i
\(133\) 3.76821 6.52674i 0.326746 0.565940i
\(134\) −6.43639 11.1481i −0.556019 0.963053i
\(135\) 2.87074 2.87074i 0.247074 0.247074i
\(136\) −11.5797 3.10277i −0.992950 0.266060i
\(137\) −0.412718 + 1.54028i −0.0352609 + 0.131595i −0.981313 0.192420i \(-0.938366\pi\)
0.946052 + 0.324016i \(0.105033\pi\)
\(138\) 2.86447 2.86447i 0.243840 0.243840i
\(139\) −15.9754 + 9.22341i −1.35502 + 0.782319i −0.988947 0.148268i \(-0.952630\pi\)
−0.366069 + 0.930588i \(0.619297\pi\)
\(140\) 2.12212 3.67562i 0.179352 0.310646i
\(141\) 4.53028 1.21389i 0.381519 0.102228i
\(142\) −14.3345 −1.20293
\(143\) 8.45979 8.45174i 0.707443 0.706770i
\(144\) 2.84540 0.237117
\(145\) 14.3963 3.85748i 1.19555 0.320346i
\(146\) −8.84875 + 15.3265i −0.732327 + 1.26843i
\(147\) −1.73812 + 1.00350i −0.143358 + 0.0827676i
\(148\) 2.96960 2.96960i 0.244100 0.244100i
\(149\) −3.81646 + 14.2432i −0.312657 + 1.16685i 0.613495 + 0.789699i \(0.289763\pi\)
−0.926151 + 0.377152i \(0.876903\pi\)
\(150\) 13.7285 + 3.67853i 1.12093 + 0.300351i
\(151\) −16.8286 + 16.8286i −1.36949 + 1.36949i −0.508333 + 0.861161i \(0.669738\pi\)
−0.861161 + 0.508333i \(0.830262\pi\)
\(152\) −5.15139 8.92248i −0.417833 0.723708i
\(153\) −1.96225 + 3.39871i −0.158638 + 0.274770i
\(154\) 8.30131 + 3.90361i 0.668939 + 0.314562i
\(155\) 9.57307i 0.768927i
\(156\) −1.58672 0.572584i −0.127039 0.0458434i
\(157\) −7.76994 −0.620109 −0.310054 0.950719i \(-0.600347\pi\)
−0.310054 + 0.950719i \(0.600347\pi\)
\(158\) −2.94373 10.9861i −0.234190 0.874011i
\(159\) −2.69770 + 4.67255i −0.213941 + 0.370557i
\(160\) −5.25216 9.09701i −0.415220 0.719182i
\(161\) −5.17100 5.17100i −0.407532 0.407532i
\(162\) 0.320366 1.19562i 0.0251703 0.0939369i
\(163\) 0.580557 2.16667i 0.0454727 0.169706i −0.939455 0.342672i \(-0.888668\pi\)
0.984928 + 0.172965i \(0.0553348\pi\)
\(164\) 0.718797 0.718797i 0.0561286 0.0561286i
\(165\) 2.38092 13.2528i 0.185354 1.03173i
\(166\) −6.85298 3.95657i −0.531894 0.307089i
\(167\) −5.81043 21.6848i −0.449624 1.67802i −0.703429 0.710766i \(-0.748349\pi\)
0.253805 0.967256i \(-0.418318\pi\)
\(168\) 6.82574i 0.526618i
\(169\) −10.0044 8.30136i −0.769567 0.638566i
\(170\) −19.7216 −1.51258
\(171\) −3.25783 + 0.872934i −0.249133 + 0.0667549i
\(172\) 4.41738 + 2.55038i 0.336822 + 0.194464i
\(173\) 6.13625 + 10.6283i 0.466531 + 0.808055i 0.999269 0.0382251i \(-0.0121704\pi\)
−0.532738 + 0.846280i \(0.678837\pi\)
\(174\) 3.21317 3.21317i 0.243590 0.243590i
\(175\) 6.64057 24.7829i 0.501980 1.87341i
\(176\) 7.74787 5.38796i 0.584018 0.406133i
\(177\) 0.0576886 + 0.0576886i 0.00433614 + 0.00433614i
\(178\) 17.5782 10.1488i 1.31754 0.760684i
\(179\) −0.737785 0.425960i −0.0551446 0.0318378i 0.472174 0.881505i \(-0.343469\pi\)
−0.527319 + 0.849667i \(0.676803\pi\)
\(180\) −1.83469 + 0.491604i −0.136750 + 0.0366420i
\(181\) 19.0384i 1.41511i 0.706656 + 0.707557i \(0.250203\pi\)
−0.706656 + 0.707557i \(0.749797\pi\)
\(182\) 3.38501 9.38039i 0.250913 0.695320i
\(183\) 2.38377i 0.176213i
\(184\) −9.65656 + 2.58747i −0.711891 + 0.190751i
\(185\) 18.2214 31.5604i 1.33966 2.32036i
\(186\) 1.45936 + 2.52769i 0.107005 + 0.185339i
\(187\) 1.09260 + 12.9701i 0.0798990 + 0.948470i
\(188\) −2.11951 0.567922i −0.154581 0.0414199i
\(189\) −2.15836 0.578331i −0.156998 0.0420674i
\(190\) −11.9847 11.9847i −0.869465 0.869465i
\(191\) 1.40927 + 2.44093i 0.101971 + 0.176619i 0.912497 0.409084i \(-0.134152\pi\)
−0.810525 + 0.585703i \(0.800818\pi\)
\(192\) −7.70196 4.44673i −0.555841 0.320915i
\(193\) −3.34419 12.4807i −0.240720 0.898379i −0.975487 0.220059i \(-0.929375\pi\)
0.734767 0.678320i \(-0.237292\pi\)
\(194\) 5.94097 0.426536
\(195\) −14.5857 1.23569i −1.04450 0.0884896i
\(196\) 0.938986 0.0670704
\(197\) −12.4413 + 3.33364i −0.886407 + 0.237512i −0.673169 0.739488i \(-0.735067\pi\)
−0.213238 + 0.977000i \(0.568401\pi\)
\(198\) −1.39165 3.86224i −0.0989004 0.274478i
\(199\) −15.7183 + 9.07499i −1.11424 + 0.643309i −0.939925 0.341381i \(-0.889106\pi\)
−0.174318 + 0.984689i \(0.555772\pi\)
\(200\) −24.8018 24.8018i −1.75375 1.75375i
\(201\) 10.0454 + 2.69165i 0.708546 + 0.189854i
\(202\) −3.84182 + 14.3379i −0.270310 + 1.00881i
\(203\) −5.80048 5.80048i −0.407114 0.407114i
\(204\) 1.59010 0.918045i 0.111329 0.0642760i
\(205\) 4.41052 7.63924i 0.308044 0.533548i
\(206\) 1.04197 + 3.88868i 0.0725975 + 0.270937i
\(207\) 3.27272i 0.227470i
\(208\) −6.61610 7.84088i −0.458744 0.543668i
\(209\) −7.21793 + 8.54587i −0.499275 + 0.591130i
\(210\) −2.90627 10.8463i −0.200551 0.748468i
\(211\) −17.3342 10.0079i −1.19334 0.688974i −0.234276 0.972170i \(-0.575272\pi\)
−0.959062 + 0.283196i \(0.908605\pi\)
\(212\) 2.18607 1.26213i 0.150140 0.0866834i
\(213\) 8.18876 8.18876i 0.561084 0.561084i
\(214\) 7.67036 + 2.05527i 0.524335 + 0.140495i
\(215\) 42.7540 + 11.4559i 2.91580 + 0.781286i
\(216\) −2.16000 + 2.16000i −0.146970 + 0.146970i
\(217\) 4.56303 2.63447i 0.309759 0.178839i
\(218\) 1.11890 + 0.645996i 0.0757814 + 0.0437524i
\(219\) −3.70048 13.8104i −0.250055 0.933219i
\(220\) −4.06487 + 4.81272i −0.274053 + 0.324473i
\(221\) 13.9282 2.49541i 0.936911 0.167860i
\(222\) 11.1110i 0.745720i
\(223\) −1.44205 5.38182i −0.0965671 0.360393i 0.900685 0.434472i \(-0.143065\pi\)
−0.997252 + 0.0740788i \(0.976398\pi\)
\(224\) −2.89075 + 5.00692i −0.193146 + 0.334539i
\(225\) −9.94395 + 5.74114i −0.662930 + 0.382743i
\(226\) −11.5299 11.5299i −0.766956 0.766956i
\(227\) −0.131308 + 0.490047i −0.00871521 + 0.0325256i −0.970147 0.242520i \(-0.922026\pi\)
0.961431 + 0.275045i \(0.0886928\pi\)
\(228\) 1.52419 + 0.408406i 0.100942 + 0.0270473i
\(229\) −9.17189 9.17189i −0.606096 0.606096i 0.335828 0.941923i \(-0.390984\pi\)
−0.941923 + 0.335828i \(0.890984\pi\)
\(230\) −14.2429 + 8.22314i −0.939149 + 0.542218i
\(231\) −6.97220 + 2.51224i −0.458737 + 0.165293i
\(232\) −10.8321 + 2.90245i −0.711161 + 0.190555i
\(233\) 28.3075 1.85448 0.927242 0.374462i \(-0.122173\pi\)
0.927242 + 0.374462i \(0.122173\pi\)
\(234\) −4.03960 + 1.89723i −0.264077 + 0.124026i
\(235\) −19.0410 −1.24210
\(236\) −0.00987897 0.0368688i −0.000643066 0.00239995i
\(237\) 7.95760 + 4.59432i 0.516902 + 0.298433i
\(238\) 5.42730 + 9.40037i 0.351800 + 0.609335i
\(239\) 13.8092 + 13.8092i 0.893241 + 0.893241i 0.994827 0.101586i \(-0.0323915\pi\)
−0.101586 + 0.994827i \(0.532392\pi\)
\(240\) −11.1583 2.98985i −0.720263 0.192994i
\(241\) 1.48430 + 0.397717i 0.0956121 + 0.0256192i 0.306308 0.951932i \(-0.400906\pi\)
−0.210696 + 0.977552i \(0.567573\pi\)
\(242\) −11.1028 7.88147i −0.713715 0.506640i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0.557628 0.965839i 0.0356984 0.0618315i
\(245\) 7.87048 2.10889i 0.502827 0.134732i
\(246\) 2.68944i 0.171472i
\(247\) 9.98056 + 6.94765i 0.635048 + 0.442069i
\(248\) 7.20298i 0.457389i
\(249\) 6.17508 1.65461i 0.391330 0.104856i
\(250\) −28.2109 16.2876i −1.78422 1.03012i
\(251\) −9.69326 + 5.59640i −0.611833 + 0.353242i −0.773683 0.633574i \(-0.781587\pi\)
0.161850 + 0.986815i \(0.448254\pi\)
\(252\) 0.739224 + 0.739224i 0.0465667 + 0.0465667i
\(253\) 6.19711 + 8.91143i 0.389609 + 0.560257i
\(254\) 1.06418 3.97156i 0.0667724 0.249198i
\(255\) 11.2662 11.2662i 0.705517 0.705517i
\(256\) 5.28307 + 9.15055i 0.330192 + 0.571909i
\(257\) 17.3300 + 10.0055i 1.08102 + 0.624126i 0.931171 0.364583i \(-0.118789\pi\)
0.149847 + 0.988709i \(0.452122\pi\)
\(258\) 13.0352 3.49277i 0.811537 0.217451i
\(259\) −20.0578 −1.24633
\(260\) 5.62068 + 3.91266i 0.348580 + 0.242653i
\(261\) 3.67112i 0.227237i
\(262\) 4.13319 + 15.4253i 0.255349 + 0.952977i
\(263\) −9.53801 5.50677i −0.588139 0.339562i 0.176222 0.984350i \(-0.443612\pi\)
−0.764361 + 0.644788i \(0.776946\pi\)
\(264\) −1.79145 + 9.97167i −0.110256 + 0.613714i
\(265\) 15.4888 15.4888i 0.951468 0.951468i
\(266\) −2.41442 + 9.01072i −0.148037 + 0.552483i
\(267\) −4.24415 + 15.8394i −0.259738 + 0.969354i
\(268\) −3.44047 3.44047i −0.210160 0.210160i
\(269\) −5.73177 9.92772i −0.349472 0.605304i 0.636683 0.771125i \(-0.280306\pi\)
−0.986156 + 0.165821i \(0.946973\pi\)
\(270\) −2.51263 + 4.35201i −0.152914 + 0.264855i
\(271\) −2.51105 9.37136i −0.152535 0.569269i −0.999304 0.0373079i \(-0.988122\pi\)
0.846769 0.531961i \(-0.178545\pi\)
\(272\) 11.1668 0.677085
\(273\) 3.42493 + 7.29238i 0.207286 + 0.441355i
\(274\) 1.97382i 0.119243i
\(275\) −16.2056 + 34.4623i −0.977232 + 2.07816i
\(276\) 0.765578 1.32602i 0.0460824 0.0798170i
\(277\) −3.63249 6.29165i −0.218255 0.378029i 0.736020 0.676960i \(-0.236703\pi\)
−0.954275 + 0.298932i \(0.903370\pi\)
\(278\) 16.1457 16.1457i 0.968354 0.968354i
\(279\) −2.27765 0.610293i −0.136359 0.0365373i
\(280\) −7.17224 + 26.7672i −0.428623 + 1.59964i
\(281\) −4.42582 + 4.42582i −0.264022 + 0.264022i −0.826686 0.562664i \(-0.809777\pi\)
0.562664 + 0.826686i \(0.309777\pi\)
\(282\) −5.02762 + 2.90270i −0.299390 + 0.172853i
\(283\) 3.67452 6.36445i 0.218427 0.378327i −0.735900 0.677090i \(-0.763241\pi\)
0.954327 + 0.298763i \(0.0965740\pi\)
\(284\) −5.23344 + 1.40230i −0.310547 + 0.0832109i
\(285\) 13.6929 0.811095
\(286\) −7.40706 + 12.8153i −0.437989 + 0.757785i
\(287\) −4.85503 −0.286583
\(288\) 2.49921 0.669662i 0.147268 0.0394602i
\(289\) 0.799174 1.38421i 0.0470102 0.0814241i
\(290\) −15.9767 + 9.22418i −0.938187 + 0.541662i
\(291\) −3.39384 + 3.39384i −0.198951 + 0.198951i
\(292\) −1.73128 + 6.46124i −0.101316 + 0.378115i
\(293\) −8.50551 2.27904i −0.496897 0.133143i 0.00166243 0.999999i \(-0.499471\pi\)
−0.498560 + 0.866855i \(0.666137\pi\)
\(294\) 1.75664 1.75664i 0.102450 0.102450i
\(295\) −0.165609 0.286843i −0.00964212 0.0167006i
\(296\) −13.7101 + 23.7467i −0.796886 + 1.38025i
\(297\) 3.00135 + 1.41135i 0.174156 + 0.0818950i
\(298\) 18.2522i 1.05732i
\(299\) 9.01841 7.60969i 0.521548 0.440080i
\(300\) 5.37203 0.310155
\(301\) −6.30523 23.5314i −0.363427 1.35633i
\(302\) 14.7293 25.5120i 0.847579 1.46805i
\(303\) −5.99600 10.3854i −0.344461 0.596624i
\(304\) 6.78601 + 6.78601i 0.389204 + 0.389204i
\(305\) 2.50478 9.34795i 0.143423 0.535262i
\(306\) 1.25727 4.69221i 0.0718736 0.268236i
\(307\) 3.35570 3.35570i 0.191520 0.191520i −0.604833 0.796353i \(-0.706760\pi\)
0.796353 + 0.604833i \(0.206760\pi\)
\(308\) 3.41263 + 0.613094i 0.194453 + 0.0349342i
\(309\) −2.81669 1.62622i −0.160236 0.0925123i
\(310\) −3.06688 11.4458i −0.174187 0.650076i
\(311\) 28.4281i 1.61201i −0.591911 0.806004i \(-0.701626\pi\)
0.591911 0.806004i \(-0.298374\pi\)
\(312\) 10.9746 + 0.929759i 0.621314 + 0.0526373i
\(313\) 5.44502 0.307771 0.153885 0.988089i \(-0.450821\pi\)
0.153885 + 0.988089i \(0.450821\pi\)
\(314\) 9.28991 2.48922i 0.524260 0.140475i
\(315\) 7.85633 + 4.53586i 0.442654 + 0.255567i
\(316\) −2.14947 3.72300i −0.120917 0.209435i
\(317\) −15.5021 + 15.5021i −0.870687 + 0.870687i −0.992547 0.121861i \(-0.961114\pi\)
0.121861 + 0.992547i \(0.461114\pi\)
\(318\) 1.72850 6.45086i 0.0969296 0.361746i
\(319\) 6.95151 + 9.99625i 0.389210 + 0.559682i
\(320\) 25.5308 + 25.5308i 1.42722 + 1.42722i
\(321\) −5.55588 + 3.20769i −0.310099 + 0.179036i
\(322\) 7.83917 + 4.52595i 0.436860 + 0.252221i
\(323\) −12.7853 + 3.42582i −0.711396 + 0.190618i
\(324\) 0.467854i 0.0259919i
\(325\) 38.9420 + 14.0526i 2.16011 + 0.779499i
\(326\) 2.77650i 0.153776i
\(327\) −1.00822 + 0.270151i −0.0557545 + 0.0149394i
\(328\) −3.31857 + 5.74793i −0.183237 + 0.317376i
\(329\) 5.24001 + 9.07597i 0.288891 + 0.500374i
\(330\) 1.39906 + 16.6081i 0.0770159 + 0.914245i
\(331\) 18.6303 + 4.99196i 1.02401 + 0.274383i 0.731473 0.681871i \(-0.238833\pi\)
0.292539 + 0.956254i \(0.405500\pi\)
\(332\) −2.88904 0.774115i −0.158556 0.0424851i
\(333\) 6.34728 + 6.34728i 0.347829 + 0.347829i
\(334\) 13.8941 + 24.0654i 0.760254 + 1.31680i
\(335\) −36.5646 21.1106i −1.99774 1.15340i
\(336\) 1.64559 + 6.14141i 0.0897741 + 0.335042i
\(337\) −10.2756 −0.559750 −0.279875 0.960037i \(-0.590293\pi\)
−0.279875 + 0.960037i \(0.590293\pi\)
\(338\) 14.6209 + 6.72023i 0.795273 + 0.365532i
\(339\) 13.1731 0.715467
\(340\) −7.20023 + 1.92930i −0.390487 + 0.104631i
\(341\) −7.35753 + 2.65108i −0.398432 + 0.143564i
\(342\) 3.61548 2.08740i 0.195503 0.112874i
\(343\) −14.2313 14.2313i −0.768420 0.768420i
\(344\) −32.1690 8.61965i −1.73444 0.464741i
\(345\) 3.43886 12.8340i 0.185142 0.690958i
\(346\) −10.7416 10.7416i −0.577471 0.577471i
\(347\) 13.2733 7.66336i 0.712549 0.411391i −0.0994550 0.995042i \(-0.531710\pi\)
0.812004 + 0.583652i \(0.198377\pi\)
\(348\) 0.858775 1.48744i 0.0460351 0.0797352i
\(349\) 6.42431 + 23.9758i 0.343885 + 1.28340i 0.893909 + 0.448248i \(0.147952\pi\)
−0.550024 + 0.835149i \(0.685381\pi\)
\(350\) 31.7584i 1.69756i
\(351\) 1.22385 3.39149i 0.0653244 0.181024i
\(352\) 5.53716 6.55587i 0.295132 0.349429i
\(353\) −4.33238 16.1687i −0.230589 0.860571i −0.980088 0.198565i \(-0.936372\pi\)
0.749499 0.662006i \(-0.230295\pi\)
\(354\) −0.0874552 0.0504923i −0.00464819 0.00268363i
\(355\) −40.7167 + 23.5078i −2.16102 + 1.24766i
\(356\) 5.42487 5.42487i 0.287518 0.287518i
\(357\) −8.47048 2.26966i −0.448305 0.120123i
\(358\) 1.01858 + 0.272926i 0.0538334 + 0.0144246i
\(359\) −1.16120 + 1.16120i −0.0612860 + 0.0612860i −0.737086 0.675799i \(-0.763799\pi\)
0.675799 + 0.737086i \(0.263799\pi\)
\(360\) 10.7401 6.20081i 0.566054 0.326811i
\(361\) 6.60301 + 3.81225i 0.347527 + 0.200645i
\(362\) −6.09926 22.7627i −0.320570 1.19638i
\(363\) 10.8450 1.84022i 0.569214 0.0965864i
\(364\) 0.318194 3.75586i 0.0166779 0.196861i
\(365\) 58.0457i 3.03825i
\(366\) −0.763678 2.85008i −0.0399181 0.148976i
\(367\) 2.73236 4.73258i 0.142628 0.247039i −0.785858 0.618408i \(-0.787778\pi\)
0.928485 + 0.371369i \(0.121111\pi\)
\(368\) 8.06461 4.65611i 0.420397 0.242716i
\(369\) 1.53637 + 1.53637i 0.0799803 + 0.0799803i
\(370\) −11.6750 + 43.5718i −0.606955 + 2.26519i
\(371\) −11.6452 3.12033i −0.604590 0.161999i
\(372\) 0.780078 + 0.780078i 0.0404451 + 0.0404451i
\(373\) 23.8570 13.7739i 1.23527 0.713183i 0.267146 0.963656i \(-0.413919\pi\)
0.968124 + 0.250473i \(0.0805861\pi\)
\(374\) −5.46153 15.1573i −0.282409 0.783768i
\(375\) 25.4203 6.81135i 1.31270 0.351737i
\(376\) 14.3269 0.738852
\(377\) 10.1163 8.53605i 0.521014 0.439629i
\(378\) 2.76586 0.142261
\(379\) 7.88764 + 29.4371i 0.405161 + 1.51208i 0.803759 + 0.594955i \(0.202830\pi\)
−0.398599 + 0.917125i \(0.630503\pi\)
\(380\) −5.54798 3.20313i −0.284605 0.164317i
\(381\) 1.66088 + 2.87672i 0.0850893 + 0.147379i
\(382\) −2.46695 2.46695i −0.126220 0.126220i
\(383\) −10.5630 2.83034i −0.539743 0.144624i −0.0213593 0.999772i \(-0.506799\pi\)
−0.518384 + 0.855148i \(0.673466\pi\)
\(384\) 5.63479 + 1.50984i 0.287549 + 0.0770486i
\(385\) 29.9813 2.52562i 1.52799 0.128717i
\(386\) 7.99677 + 13.8508i 0.407025 + 0.704988i
\(387\) −5.45123 + 9.44180i −0.277101 + 0.479954i
\(388\) 2.16901 0.581184i 0.110115 0.0295051i
\(389\) 25.5029i 1.29305i −0.762895 0.646523i \(-0.776222\pi\)
0.762895 0.646523i \(-0.223778\pi\)
\(390\) 17.8349 3.19534i 0.903103 0.161803i
\(391\) 12.8438i 0.649538i
\(392\) −5.92191 + 1.58677i −0.299102 + 0.0801441i
\(393\) −11.1730 6.45073i −0.563603 0.325396i
\(394\) 13.8071 7.97155i 0.695593 0.401601i
\(395\) −26.3782 26.3782i −1.32723 1.32723i
\(396\) −0.885913 1.27394i −0.0445188 0.0640178i
\(397\) 0.244082 0.910927i 0.0122501 0.0457181i −0.959530 0.281606i \(-0.909133\pi\)
0.971780 + 0.235888i \(0.0757997\pi\)
\(398\) 15.8859 15.8859i 0.796287 0.796287i
\(399\) −3.76821 6.52674i −0.188647 0.326746i
\(400\) 28.2946 + 16.3359i 1.41473 + 0.816794i
\(401\) 5.49830 1.47327i 0.274572 0.0735714i −0.118906 0.992906i \(-0.537939\pi\)
0.393478 + 0.919334i \(0.371272\pi\)
\(402\) −12.8728 −0.642036
\(403\) 3.61421 + 7.69540i 0.180037 + 0.383335i
\(404\) 5.61050i 0.279133i
\(405\) −1.05076 3.92150i −0.0522129 0.194861i
\(406\) 8.79346 + 5.07691i 0.436412 + 0.251963i
\(407\) 29.3023 + 5.26427i 1.45246 + 0.260940i
\(408\) −8.47692 + 8.47692i −0.419670 + 0.419670i
\(409\) −4.15597 + 15.5103i −0.205500 + 0.766935i 0.783797 + 0.621017i \(0.213280\pi\)
−0.989297 + 0.145918i \(0.953386\pi\)
\(410\) −2.82596 + 10.5466i −0.139564 + 0.520861i
\(411\) 1.12757 + 1.12757i 0.0556187 + 0.0556187i
\(412\) 0.760833 + 1.31780i 0.0374835 + 0.0649234i
\(413\) −0.0911497 + 0.157876i −0.00448519 + 0.00776857i
\(414\) −1.04847 3.91294i −0.0515294 0.192310i
\(415\) −25.9542 −1.27404
\(416\) −7.65648 5.32982i −0.375390 0.261316i
\(417\) 18.4468i 0.903344i
\(418\) 5.89211 12.5300i 0.288193 0.612863i
\(419\) −10.8437 + 18.7818i −0.529748 + 0.917550i 0.469650 + 0.882853i \(0.344380\pi\)
−0.999398 + 0.0346972i \(0.988953\pi\)
\(420\) −2.12212 3.67562i −0.103549 0.179352i
\(421\) 23.1006 23.1006i 1.12585 1.12585i 0.135011 0.990844i \(-0.456893\pi\)
0.990844 0.135011i \(-0.0431068\pi\)
\(422\) 23.9314 + 6.41240i 1.16496 + 0.312151i
\(423\) 1.21389 4.53028i 0.0590212 0.220270i
\(424\) −11.6541 + 11.6541i −0.565972 + 0.565972i
\(425\) −39.0250 + 22.5311i −1.89299 + 1.09292i
\(426\) −7.16726 + 12.4141i −0.347255 + 0.601463i
\(427\) −5.14503 + 1.37861i −0.248986 + 0.0667155i
\(428\) 3.00146 0.145081
\(429\) −3.08953 11.5523i −0.149164 0.557749i
\(430\) −54.7877 −2.64210
\(431\) −22.5285 + 6.03650i −1.08516 + 0.290768i −0.756709 0.653752i \(-0.773194\pi\)
−0.328453 + 0.944520i \(0.606527\pi\)
\(432\) 1.42270 2.46419i 0.0684498 0.118559i
\(433\) 24.7531 14.2912i 1.18956 0.686793i 0.231354 0.972870i \(-0.425685\pi\)
0.958207 + 0.286077i \(0.0923512\pi\)
\(434\) −4.61167 + 4.61167i −0.221367 + 0.221367i
\(435\) 3.85748 14.3963i 0.184952 0.690250i
\(436\) 0.471698 + 0.126391i 0.0225902 + 0.00605304i
\(437\) −7.80511 + 7.80511i −0.373369 + 0.373369i
\(438\) 8.84875 + 15.3265i 0.422809 + 0.732327i
\(439\) −3.72237 + 6.44733i −0.177659 + 0.307714i −0.941078 0.338189i \(-0.890186\pi\)
0.763419 + 0.645903i \(0.223519\pi\)
\(440\) 17.5031 37.2215i 0.834425 1.77447i
\(441\) 2.00701i 0.0955718i
\(442\) −15.8534 + 7.44569i −0.754069 + 0.354155i
\(443\) 32.8625 1.56134 0.780672 0.624941i \(-0.214877\pi\)
0.780672 + 0.624941i \(0.214877\pi\)
\(444\) −1.08695 4.05655i −0.0515843 0.192515i
\(445\) 33.2869 57.6545i 1.57795 2.73309i
\(446\) 3.44830 + 5.97264i 0.163282 + 0.282813i
\(447\) 10.4268 + 10.4268i 0.493169 + 0.493169i
\(448\) 5.14337 19.1953i 0.243001 0.906893i
\(449\) −3.74288 + 13.9686i −0.176637 + 0.659220i 0.819630 + 0.572894i \(0.194179\pi\)
−0.996267 + 0.0863259i \(0.972487\pi\)
\(450\) 10.0499 10.0499i 0.473759 0.473759i
\(451\) 7.09267 + 1.27423i 0.333981 + 0.0600010i
\(452\) −5.33741 3.08155i −0.251051 0.144944i
\(453\) 6.15970 + 22.9883i 0.289408 + 1.08009i
\(454\) 0.627978i 0.0294725i
\(455\) −5.76830 32.1959i −0.270422 1.50937i
\(456\) −10.3028 −0.482472
\(457\) 8.23691 2.20707i 0.385307 0.103243i −0.0609656 0.998140i \(-0.519418\pi\)
0.446272 + 0.894897i \(0.352751\pi\)
\(458\) 13.9045 + 8.02775i 0.649713 + 0.375112i
\(459\) 1.96225 + 3.39871i 0.0915898 + 0.158638i
\(460\) −4.39555 + 4.39555i −0.204943 + 0.204943i
\(461\) 8.60468 32.1131i 0.400760 1.49566i −0.410984 0.911643i \(-0.634815\pi\)
0.811744 0.584014i \(-0.198519\pi\)
\(462\) 7.53128 5.23734i 0.350387 0.243663i
\(463\) −17.1423 17.1423i −0.796668 0.796668i 0.185900 0.982569i \(-0.440480\pi\)
−0.982569 + 0.185900i \(0.940480\pi\)
\(464\) 9.04635 5.22291i 0.419966 0.242468i
\(465\) 8.29052 + 4.78653i 0.384464 + 0.221970i
\(466\) −33.8450 + 9.06875i −1.56784 + 0.420102i
\(467\) 6.84310i 0.316661i −0.987386 0.158330i \(-0.949389\pi\)
0.987386 0.158330i \(-0.0506111\pi\)
\(468\) −1.28923 + 1.08785i −0.0595948 + 0.0502858i
\(469\) 23.2382i 1.07304i
\(470\) 22.7659 6.10010i 1.05011 0.281376i
\(471\) −3.88497 + 6.72897i −0.179010 + 0.310054i
\(472\) 0.124608 + 0.215827i 0.00573553 + 0.00993423i
\(473\) 3.03531 + 36.0317i 0.139564 + 1.65674i
\(474\) −10.9861 2.94373i −0.504610 0.135210i
\(475\) −37.4074 10.0233i −1.71637 0.459900i
\(476\) 2.90108 + 2.90108i 0.132971 + 0.132971i
\(477\) 2.69770 + 4.67255i 0.123519 + 0.213941i
\(478\) −20.9345 12.0866i −0.957524 0.552827i
\(479\) 3.08908 + 11.5286i 0.141144 + 0.526756i 0.999897 + 0.0143661i \(0.00457303\pi\)
−0.858753 + 0.512390i \(0.828760\pi\)
\(480\) −10.5043 −0.479455
\(481\) 2.73214 32.2494i 0.124575 1.47044i
\(482\) −1.90207 −0.0866371
\(483\) −7.06372 + 1.89272i −0.321410 + 0.0861216i
\(484\) −4.82458 1.79133i −0.219299 0.0814239i
\(485\) 16.8751 9.74284i 0.766259 0.442400i
\(486\) −0.875256 0.875256i −0.0397024 0.0397024i
\(487\) 12.4957 + 3.34820i 0.566232 + 0.151721i 0.530568 0.847642i \(-0.321979\pi\)
0.0356642 + 0.999364i \(0.488645\pi\)
\(488\) −1.88465 + 7.03359i −0.0853139 + 0.318396i
\(489\) −1.58611 1.58611i −0.0717264 0.0717264i
\(490\) −8.73450 + 5.04287i −0.394585 + 0.227814i
\(491\) −8.24322 + 14.2777i −0.372012 + 0.644343i −0.989875 0.141943i \(-0.954665\pi\)
0.617863 + 0.786285i \(0.287998\pi\)
\(492\) −0.263098 0.981895i −0.0118614 0.0442673i
\(493\) 14.4073i 0.648872i
\(494\) −14.1588 5.10933i −0.637033 0.229880i
\(495\) −10.2868 8.68833i −0.462357 0.390511i
\(496\) 1.73653 + 6.48082i 0.0779726 + 0.290998i
\(497\) 22.4101 + 12.9385i 1.00523 + 0.580370i
\(498\) −6.85298 + 3.95657i −0.307089 + 0.177298i
\(499\) 4.14952 4.14952i 0.185758 0.185758i −0.608101 0.793859i \(-0.708069\pi\)
0.793859 + 0.608101i \(0.208069\pi\)
\(500\) −11.8930 3.18672i −0.531871 0.142514i
\(501\) −21.6848 5.81043i −0.968806 0.259591i
\(502\) 9.79657 9.79657i 0.437242 0.437242i
\(503\) 27.7109 15.9989i 1.23557 0.713355i 0.267382 0.963591i \(-0.413841\pi\)
0.968185 + 0.250235i \(0.0805080\pi\)
\(504\) −5.91127 3.41287i −0.263309 0.152021i
\(505\) 12.6007 + 47.0266i 0.560726 + 2.09266i
\(506\) −10.2643 8.66935i −0.456305 0.385400i
\(507\) −12.1914 + 4.51336i −0.541438 + 0.200445i
\(508\) 1.55410i 0.0689518i
\(509\) 9.23809 + 34.4770i 0.409471 + 1.52817i 0.795657 + 0.605747i \(0.207126\pi\)
−0.386186 + 0.922421i \(0.626208\pi\)
\(510\) −9.86081 + 17.0794i −0.436644 + 0.756289i
\(511\) 27.6677 15.9739i 1.22395 0.706646i
\(512\) −17.4980 17.4980i −0.773309 0.773309i
\(513\) −0.872934 + 3.25783i −0.0385410 + 0.143837i
\(514\) −23.9256 6.41084i −1.05531 0.282770i
\(515\) 9.33690 + 9.33690i 0.411433 + 0.411433i
\(516\) 4.41738 2.55038i 0.194464 0.112274i
\(517\) −5.27305 14.6343i −0.231909 0.643615i
\(518\) 23.9815 6.42583i 1.05369 0.282335i
\(519\) 12.2725 0.538703
\(520\) −42.0599 15.1777i −1.84445 0.665588i
\(521\) −22.0414 −0.965649 −0.482825 0.875717i \(-0.660389\pi\)
−0.482825 + 0.875717i \(0.660389\pi\)
\(522\) −1.17610 4.38927i −0.0514766 0.192113i
\(523\) −1.63698 0.945111i −0.0715802 0.0413268i 0.463783 0.885949i \(-0.346492\pi\)
−0.535363 + 0.844622i \(0.679825\pi\)
\(524\) 3.01800 + 5.22733i 0.131842 + 0.228357i
\(525\) −18.1424 18.1424i −0.791798 0.791798i
\(526\) 13.1680 + 3.52836i 0.574154 + 0.153844i
\(527\) −8.93861 2.39509i −0.389372 0.104332i
\(528\) −0.792177 9.40383i −0.0344751 0.409249i
\(529\) −6.14465 10.6428i −0.267159 0.462732i
\(530\) −13.5566 + 23.4808i −0.588863 + 1.01994i
\(531\) 0.0788041 0.0211155i 0.00341981 0.000916334i
\(532\) 3.52595i 0.152869i
\(533\) 0.661321 7.80602i 0.0286450 0.338116i
\(534\) 20.2976i 0.878362i
\(535\) 25.1579 6.74104i 1.08767 0.291441i
\(536\) 27.5120 + 15.8841i 1.18834 + 0.686087i
\(537\) −0.737785 + 0.425960i −0.0318378 + 0.0183815i
\(538\) 10.0335 + 10.0335i 0.432577 + 0.432577i
\(539\) 3.80040 + 5.46496i 0.163695 + 0.235393i
\(540\) −0.491604 + 1.83469i −0.0211553 + 0.0789525i
\(541\) −2.73283 + 2.73283i −0.117494 + 0.117494i −0.763409 0.645915i \(-0.776476\pi\)
0.645915 + 0.763409i \(0.276476\pi\)
\(542\) 6.00453 + 10.4001i 0.257916 + 0.446724i
\(543\) 16.4877 + 9.51920i 0.707557 + 0.408508i
\(544\) 9.80814 2.62808i 0.420521 0.112678i
\(545\) 4.23759 0.181518
\(546\) −6.43115 7.62170i −0.275228 0.326178i
\(547\) 15.3594i 0.656719i 0.944553 + 0.328360i \(0.106496\pi\)
−0.944553 + 0.328360i \(0.893504\pi\)
\(548\) −0.193092 0.720628i −0.00824847 0.0307837i
\(549\) 2.06440 + 1.19188i 0.0881066 + 0.0508684i
\(550\) 8.33517 46.3956i 0.355413 1.97832i
\(551\) −8.75526 + 8.75526i −0.372987 + 0.372987i
\(552\) −2.58747 + 9.65656i −0.110130 + 0.411010i
\(553\) −5.31408 + 19.8324i −0.225978 + 0.843360i
\(554\) 6.35871 + 6.35871i 0.270156 + 0.270156i
\(555\) −18.2214 31.5604i −0.773454 1.33966i
\(556\) 4.31521 7.47416i 0.183006 0.316975i
\(557\) −3.20803 11.9725i −0.135928 0.507292i −0.999992 0.00390979i \(-0.998755\pi\)
0.864064 0.503382i \(-0.167911\pi\)
\(558\) 2.91872 0.123559
\(559\) 38.6932 6.93239i 1.63655 0.293209i
\(560\) 25.8127i 1.09079i
\(561\) 11.7788 + 5.53885i 0.497300 + 0.233850i
\(562\) 3.87372 6.70948i 0.163403 0.283023i
\(563\) 3.23176 + 5.59758i 0.136203 + 0.235910i 0.926056 0.377386i \(-0.123177\pi\)
−0.789854 + 0.613295i \(0.789844\pi\)
\(564\) −1.55159 + 1.55159i −0.0653337 + 0.0653337i
\(565\) −51.6585 13.8419i −2.17329 0.582331i
\(566\) −2.35438 + 8.78667i −0.0989620 + 0.369331i
\(567\) −1.58003 + 1.58003i −0.0663550 + 0.0663550i
\(568\) 30.6361 17.6877i 1.28546 0.742161i
\(569\) 21.7504 37.6729i 0.911826 1.57933i 0.100342 0.994953i \(-0.468006\pi\)
0.811483 0.584376i \(-0.198661\pi\)
\(570\) −16.3715 + 4.38672i −0.685726 + 0.183740i
\(571\) 1.31335 0.0549622 0.0274811 0.999622i \(-0.491251\pi\)
0.0274811 + 0.999622i \(0.491251\pi\)
\(572\) −1.45059 + 5.40340i −0.0606523 + 0.225927i
\(573\) 2.81854 0.117746
\(574\) 5.80478 1.55538i 0.242287 0.0649205i
\(575\) −18.7892 + 32.5438i −0.783562 + 1.35717i
\(576\) −7.70196 + 4.44673i −0.320915 + 0.185280i
\(577\) −27.1353 + 27.1353i −1.12966 + 1.12966i −0.139424 + 0.990233i \(0.544525\pi\)
−0.990233 + 0.139424i \(0.955475\pi\)
\(578\) −0.512056 + 1.91102i −0.0212987 + 0.0794880i
\(579\) −12.4807 3.34419i −0.518679 0.138980i
\(580\) −4.93064 + 4.93064i −0.204733 + 0.204733i
\(581\) 7.14248 + 12.3711i 0.296320 + 0.513242i
\(582\) 2.97048 5.14503i 0.123130 0.213268i
\(583\) 16.1935 + 7.61481i 0.670665 + 0.315373i
\(584\) 43.6748i 1.80728i
\(585\) −8.36299 + 12.0137i −0.345767 + 0.496707i
\(586\) 10.8995 0.450254
\(587\) −1.21970 4.55197i −0.0503423 0.187880i 0.936176 0.351532i \(-0.114339\pi\)
−0.986518 + 0.163652i \(0.947673\pi\)
\(588\) 0.469493 0.813186i 0.0193616 0.0335352i
\(589\) −3.97647 6.88745i −0.163848 0.283792i
\(590\) 0.289900 + 0.289900i 0.0119350 + 0.0119350i
\(591\) −3.33364 + 12.4413i −0.137128 + 0.511767i
\(592\) 6.61063 24.6712i 0.271695 1.01398i
\(593\) −5.52845 + 5.52845i −0.227026 + 0.227026i −0.811449 0.584423i \(-0.801321\pi\)
0.584423 + 0.811449i \(0.301321\pi\)
\(594\) −4.04063 0.725915i −0.165789 0.0297847i
\(595\) 30.8321 + 17.8009i 1.26399 + 0.729767i
\(596\) −1.78555 6.66375i −0.0731388 0.272958i
\(597\) 18.1500i 0.742829i
\(598\) −8.34472 + 11.9875i −0.341241 + 0.490205i
\(599\) 25.9318 1.05955 0.529773 0.848139i \(-0.322277\pi\)
0.529773 + 0.848139i \(0.322277\pi\)
\(600\) −33.8799 + 9.07808i −1.38314 + 0.370611i
\(601\) −31.1503 17.9847i −1.27065 0.733610i −0.295539 0.955331i \(-0.595499\pi\)
−0.975110 + 0.221721i \(0.928833\pi\)
\(602\) 15.0773 + 26.1147i 0.614506 + 1.06436i
\(603\) 7.35372 7.35372i 0.299467 0.299467i
\(604\) 2.88184 10.7552i 0.117260 0.437622i
\(605\) −44.4623 4.17909i −1.80765 0.169904i
\(606\) 10.4961 + 10.4961i 0.426373 + 0.426373i
\(607\) 13.1072 7.56746i 0.532006 0.307154i −0.209827 0.977739i \(-0.567290\pi\)
0.741833 + 0.670585i \(0.233957\pi\)
\(608\) 7.55745 + 4.36330i 0.306495 + 0.176955i
\(609\) −7.92361 + 2.12312i −0.321081 + 0.0860334i
\(610\) 11.9791i 0.485018i
\(611\) −15.3063 + 7.18874i −0.619227 + 0.290825i
\(612\) 1.83609i 0.0742196i
\(613\) 35.2736 9.45154i 1.42469 0.381744i 0.537544 0.843236i \(-0.319352\pi\)
0.887144 + 0.461492i \(0.152686\pi\)
\(614\) −2.93710 + 5.08720i −0.118532 + 0.205303i
\(615\) −4.41052 7.63924i −0.177849 0.308044i
\(616\) −22.5585 + 1.90033i −0.908909 + 0.0765664i
\(617\) −8.02453 2.15017i −0.323055 0.0865624i 0.0936469 0.995605i \(-0.470148\pi\)
−0.416702 + 0.909043i \(0.636814\pi\)
\(618\) 3.88868 + 1.04197i 0.156426 + 0.0419142i
\(619\) 0.134502 + 0.134502i 0.00540610 + 0.00540610i 0.709805 0.704399i \(-0.248783\pi\)
−0.704399 + 0.709805i \(0.748783\pi\)
\(620\) −2.23940 3.87875i −0.0899364 0.155774i
\(621\) 2.83426 + 1.63636i 0.113735 + 0.0656649i
\(622\) 9.10738 + 33.9892i 0.365173 + 1.36284i
\(623\) −36.6416 −1.46802
\(624\) −10.0985 + 1.80927i −0.404262 + 0.0724287i
\(625\) −49.4315 −1.97726
\(626\) −6.51018 + 1.74440i −0.260199 + 0.0697202i
\(627\) 3.79198 + 10.5238i 0.151437 + 0.420282i
\(628\) 3.14817 1.81760i 0.125626 0.0725301i
\(629\) 24.9099 + 24.9099i 0.993221 + 0.993221i
\(630\) −10.8463 2.90627i −0.432128 0.115788i
\(631\) −4.37954 + 16.3447i −0.174347 + 0.650671i 0.822315 + 0.569032i \(0.192682\pi\)
−0.996662 + 0.0816388i \(0.973985\pi\)
\(632\) 19.8475 + 19.8475i 0.789492 + 0.789492i
\(633\) −17.3342 + 10.0079i −0.688974 + 0.397780i
\(634\) 13.5683 23.5010i 0.538867 0.933346i
\(635\) −3.49038 13.0263i −0.138511 0.516931i
\(636\) 2.52426i 0.100093i
\(637\) 5.53057 4.66667i 0.219129 0.184900i
\(638\) −11.5138 9.72471i −0.455837 0.385005i
\(639\) −2.99729 11.1860i −0.118571 0.442513i
\(640\) −20.5104 11.8417i −0.810743 0.468083i
\(641\) −6.32581 + 3.65221i −0.249854 + 0.144253i −0.619698 0.784841i \(-0.712745\pi\)
0.369843 + 0.929094i \(0.379411\pi\)
\(642\) 5.61509 5.61509i 0.221610 0.221610i
\(643\) −21.4696 5.75275i −0.846677 0.226867i −0.190701 0.981648i \(-0.561076\pi\)
−0.655976 + 0.754782i \(0.727743\pi\)
\(644\) 3.30479 + 0.885515i 0.130227 + 0.0348942i
\(645\) 31.2981 31.2981i 1.23236 1.23236i
\(646\) 14.1889 8.19198i 0.558256 0.322309i
\(647\) −17.5217 10.1162i −0.688851 0.397708i 0.114331 0.993443i \(-0.463528\pi\)
−0.803181 + 0.595735i \(0.796861\pi\)
\(648\) 0.790616 + 2.95062i 0.0310583 + 0.115911i
\(649\) 0.174595 0.206717i 0.00685346 0.00811435i
\(650\) −51.0619 4.32593i −2.00281 0.169677i
\(651\) 5.26894i 0.206506i
\(652\) 0.271616 + 1.01368i 0.0106373 + 0.0396989i
\(653\) −14.1283 + 24.4710i −0.552885 + 0.957625i 0.445180 + 0.895441i \(0.353140\pi\)
−0.998065 + 0.0621835i \(0.980194\pi\)
\(654\) 1.11890 0.645996i 0.0437524 0.0252605i
\(655\) 37.0367 + 37.0367i 1.44715 + 1.44715i
\(656\) 1.60012 5.97171i 0.0624740 0.233156i
\(657\) −13.8104 3.70048i −0.538794 0.144369i
\(658\) −9.17270 9.17270i −0.357589 0.357589i
\(659\) −12.8992 + 7.44733i −0.502480 + 0.290107i −0.729737 0.683728i \(-0.760358\pi\)
0.227257 + 0.973835i \(0.427024\pi\)
\(660\) 2.13550 + 5.92664i 0.0831242 + 0.230694i
\(661\) −0.160358 + 0.0429679i −0.00623722 + 0.00167126i −0.261936 0.965085i \(-0.584361\pi\)
0.255699 + 0.966756i \(0.417694\pi\)
\(662\) −23.8740 −0.927889
\(663\) 4.80300 13.3099i 0.186533 0.516913i
\(664\) 19.5285 0.757852
\(665\) 7.91900 + 29.5541i 0.307086 + 1.14606i
\(666\) −9.62240 5.55549i −0.372860 0.215271i
\(667\) 6.00728 + 10.4049i 0.232603 + 0.402880i
\(668\) 7.42689 + 7.42689i 0.287355 + 0.287355i
\(669\) −5.38182 1.44205i −0.208073 0.0557530i
\(670\) 50.4806 + 13.5262i 1.95024 + 0.522564i
\(671\) 7.87816 0.663655i 0.304133 0.0256201i
\(672\) 2.89075 + 5.00692i 0.111513 + 0.193146i
\(673\) −8.13668 + 14.0931i −0.313646 + 0.543251i −0.979149 0.203145i \(-0.934884\pi\)
0.665503 + 0.746395i \(0.268217\pi\)
\(674\) 12.2858 3.29196i 0.473230 0.126802i
\(675\) 11.4823i 0.441953i
\(676\) 5.99542 + 1.02320i 0.230593 + 0.0393538i
\(677\) 34.0774i 1.30970i −0.755759 0.654850i \(-0.772732\pi\)
0.755759 0.654850i \(-0.227268\pi\)
\(678\) −15.7501 + 4.22023i −0.604879 + 0.162077i
\(679\) −9.28791 5.36238i −0.356437 0.205789i
\(680\) 42.1495 24.3350i 1.61636 0.933206i
\(681\) 0.358740 + 0.358740i 0.0137469 + 0.0137469i
\(682\) 7.94750 5.52679i 0.304326 0.211632i
\(683\) 6.75924 25.2258i 0.258635 0.965239i −0.707397 0.706816i \(-0.750131\pi\)
0.966032 0.258422i \(-0.0832026\pi\)
\(684\) 1.11579 1.11579i 0.0426631 0.0426631i
\(685\) −3.23695 5.60656i −0.123677 0.214216i
\(686\) 21.5745 + 12.4561i 0.823720 + 0.475575i
\(687\) −12.5290 + 3.35714i −0.478012 + 0.128083i
\(688\) 31.0219 1.18270
\(689\) 6.60317 18.2984i 0.251561 0.697114i
\(690\) 16.4463i 0.626099i
\(691\) 8.90292 + 33.2261i 0.338683 + 1.26398i 0.899821 + 0.436260i \(0.143697\pi\)
−0.561138 + 0.827722i \(0.689636\pi\)
\(692\) −4.97249 2.87087i −0.189026 0.109134i
\(693\) −1.31044 + 7.29422i −0.0497794 + 0.277085i
\(694\) −13.4148 + 13.4148i −0.509219 + 0.509219i
\(695\) 19.3832 72.3392i 0.735248 2.74398i
\(696\) −2.90245 + 10.8321i −0.110017 + 0.410589i
\(697\) 6.02948 + 6.02948i 0.228383 + 0.228383i
\(698\) −15.3621 26.6079i −0.581463 1.00712i
\(699\) 14.1537 24.5150i 0.535344 0.927242i
\(700\) 3.10682 + 11.5948i 0.117427 + 0.438242i
\(701\) −16.9132 −0.638804 −0.319402 0.947619i \(-0.603482\pi\)
−0.319402 + 0.947619i \(0.603482\pi\)
\(702\) −0.376748 + 4.44702i −0.0142194 + 0.167842i
\(703\) 30.2752i 1.14185i
\(704\) −12.5518 + 26.6924i −0.473064 + 1.00601i
\(705\) −9.52052 + 16.4900i −0.358563 + 0.621050i
\(706\) 10.3598 + 17.9436i 0.389895 + 0.675318i
\(707\) 18.9477 18.9477i 0.712602 0.712602i
\(708\) −0.0368688 0.00987897i −0.00138561 0.000371274i
\(709\) 9.12665 34.0611i 0.342759 1.27919i −0.552450 0.833546i \(-0.686307\pi\)
0.895209 0.445647i \(-0.147026\pi\)
\(710\) 41.1507 41.1507i 1.54436 1.54436i
\(711\) 7.95760 4.59432i 0.298433 0.172301i
\(712\) −25.0457 + 43.3805i −0.938628 + 1.62575i
\(713\) −7.45410 + 1.99732i −0.279158 + 0.0748002i
\(714\) 10.8546 0.406224
\(715\) −0.0231114 + 48.5486i −0.000864316 + 1.81561i
\(716\) 0.398575 0.0148954
\(717\) 18.8637 5.05451i 0.704477 0.188764i
\(718\) 1.01635 1.76037i 0.0379299 0.0656965i
\(719\) −34.6625 + 20.0124i −1.29269 + 0.746336i −0.979131 0.203232i \(-0.934856\pi\)
−0.313562 + 0.949568i \(0.601522\pi\)
\(720\) −8.16841 + 8.16841i −0.304419 + 0.304419i
\(721\) 1.88099 7.01993i 0.0700516 0.261436i
\(722\) −9.11602 2.44263i −0.339263 0.0909053i
\(723\) 1.08658 1.08658i 0.0404104 0.0404104i
\(724\) −4.45360 7.71386i −0.165517 0.286683i
\(725\) −21.0764 + 36.5055i −0.782759 + 1.35578i
\(726\) −12.3770 + 5.67457i −0.459352 + 0.210603i
\(727\) 53.5442i 1.98584i −0.118766 0.992922i \(-0.537894\pi\)
0.118766 0.992922i \(-0.462106\pi\)
\(728\) 4.34019 + 24.2248i 0.160858 + 0.897832i
\(729\) 1.00000 0.0370370
\(730\) −18.5959 69.4008i −0.688264 2.56864i
\(731\) −21.3933 + 37.0543i −0.791260 + 1.37050i
\(732\) −0.557628 0.965839i −0.0206105 0.0356984i
\(733\) −24.5715 24.5715i −0.907569 0.907569i 0.0885062 0.996076i \(-0.471791\pi\)
−0.996076 + 0.0885062i \(0.971791\pi\)
\(734\) −1.75071 + 6.53373i −0.0646198 + 0.241164i
\(735\) 2.10889 7.87048i 0.0777876 0.290307i
\(736\) 5.98761 5.98761i 0.220706 0.220706i
\(737\) 6.09899 33.9485i 0.224659 1.25051i
\(738\) −2.32912 1.34472i −0.0857361 0.0494997i
\(739\) −5.26107 19.6346i −0.193532 0.722270i −0.992642 0.121085i \(-0.961362\pi\)
0.799111 0.601184i \(-0.205304\pi\)
\(740\) 17.0499i 0.626766i
\(741\) 11.0071 5.16959i 0.404357 0.189910i
\(742\) 14.9229 0.547838
\(743\) 28.7347 7.69945i 1.05418 0.282465i 0.310199 0.950672i \(-0.399604\pi\)
0.743976 + 0.668206i \(0.232938\pi\)
\(744\) −6.23796 3.60149i −0.228695 0.132037i
\(745\) −29.9325 51.8447i −1.09664 1.89944i
\(746\) −24.1113 + 24.1113i −0.882777 + 0.882777i
\(747\) 1.65461 6.17508i 0.0605389 0.225934i
\(748\) −3.47676 4.99957i −0.127123 0.182802i
\(749\) −10.1365 10.1365i −0.370379 0.370379i
\(750\) −28.2109 + 16.2876i −1.03012 + 0.594739i
\(751\) 4.06293 + 2.34573i 0.148258 + 0.0855970i 0.572294 0.820048i \(-0.306054\pi\)
−0.424036 + 0.905645i \(0.639387\pi\)
\(752\) −12.8905 + 3.45400i −0.470068 + 0.125954i
\(753\) 11.1928i 0.407889i
\(754\) −9.36056 + 13.4468i −0.340891 + 0.489703i
\(755\) 96.6211i 3.51640i
\(756\) 1.00980 0.270575i 0.0367260 0.00984070i
\(757\) 21.7081 37.5995i 0.788994 1.36658i −0.137590 0.990489i \(-0.543935\pi\)
0.926584 0.376089i \(-0.122731\pi\)
\(758\) −18.8613 32.6687i −0.685072 1.18658i
\(759\) 10.8161 0.911145i 0.392599 0.0330725i
\(760\) 40.4024 + 10.8258i 1.46555 + 0.392693i
\(761\) 42.4461 + 11.3734i 1.53867 + 0.412285i 0.925836 0.377926i \(-0.123363\pi\)
0.612834 + 0.790211i \(0.290029\pi\)
\(762\) −2.90738 2.90738i −0.105323 0.105323i
\(763\) −1.16617 2.01986i −0.0422180 0.0731238i
\(764\) −1.14200 0.659333i −0.0413161 0.0238538i
\(765\) −4.12371 15.3899i −0.149093 0.556423i
\(766\) 13.5361 0.489078
\(767\) −0.241421 0.168057i −0.00871720 0.00606820i
\(768\) 10.5661 0.381273
\(769\) −30.7278 + 8.23350i −1.10807 + 0.296907i −0.766048 0.642783i \(-0.777780\pi\)
−0.342026 + 0.939691i \(0.611113\pi\)
\(770\) −35.0371 + 12.6247i −1.26265 + 0.454961i
\(771\) 17.3300 10.0055i 0.624126 0.360339i
\(772\) 4.27454 + 4.27454i 0.153844 + 0.153844i
\(773\) 5.28534 + 1.41620i 0.190100 + 0.0509372i 0.352613 0.935769i \(-0.385293\pi\)
−0.162513 + 0.986706i \(0.551960\pi\)
\(774\) 3.49277 13.0352i 0.125545 0.468541i
\(775\) −19.1450 19.1450i −0.687709 0.687709i
\(776\) −12.6972 + 7.33072i −0.455802 + 0.263157i
\(777\) −10.0289 + 17.3706i −0.359785 + 0.623165i
\(778\) 8.17024 + 30.4918i 0.292917 + 1.09318i
\(779\) 7.32818i 0.262559i
\(780\) 6.19880 2.91132i 0.221953 0.104242i
\(781\) −29.3430 24.7834i −1.04997 0.886819i
\(782\) −4.11471 15.3563i −0.147142 0.549140i
\(783\) 3.17928 + 1.83556i 0.113618 + 0.0655976i
\(784\) 4.94565 2.85537i 0.176630 0.101978i
\(785\) 22.3055 22.3055i 0.796116 0.796116i
\(786\) 15.4253 + 4.13319i 0.550201 + 0.147426i
\(787\) −26.5978 7.12685i −0.948108 0.254045i −0.248549 0.968619i \(-0.579954\pi\)
−0.699559 + 0.714574i \(0.746620\pi\)
\(788\) 4.26106 4.26106i 0.151794 0.151794i
\(789\) −9.53801 + 5.50677i −0.339562 + 0.196046i
\(790\) 39.9890 + 23.0877i 1.42275 + 0.821423i
\(791\) 7.61844 + 28.4324i 0.270881 + 1.01094i
\(792\) 7.74000 + 6.53728i 0.275029 + 0.232292i
\(793\) −1.51573 8.46009i −0.0538253 0.300426i
\(794\) 1.16732i 0.0414266i
\(795\) −5.66929 21.1581i −0.201069 0.750399i
\(796\) 4.24577 7.35389i 0.150487 0.260652i
\(797\) −23.6364 + 13.6465i −0.837243 + 0.483383i −0.856326 0.516435i \(-0.827259\pi\)
0.0190829 + 0.999818i \(0.493925\pi\)
\(798\) 6.59631 + 6.59631i 0.233507 + 0.233507i
\(799\) 4.76389 17.7791i 0.168534 0.628978i
\(800\) 28.6967 + 7.68925i 1.01458 + 0.271856i
\(801\) 11.5952 + 11.5952i 0.409697 + 0.409697i
\(802\) −6.10190 + 3.52294i −0.215466 + 0.124399i
\(803\) −44.6119 + 16.0747i −1.57432 + 0.567263i
\(804\) −4.69977 + 1.25930i −0.165748 + 0.0444120i
\(805\) 29.6892 1.04641
\(806\) −6.78657 8.04292i −0.239047 0.283300i
\(807\) −11.4635 −0.403536
\(808\) −9.48106 35.3838i −0.333543 1.24480i
\(809\) −23.9374 13.8203i −0.841594 0.485895i 0.0162117 0.999869i \(-0.494839\pi\)
−0.857806 + 0.513974i \(0.828173\pi\)
\(810\) 2.51263 + 4.35201i 0.0882849 + 0.152914i
\(811\) −18.8788 18.8788i −0.662923 0.662923i 0.293145 0.956068i \(-0.405298\pi\)
−0.956068 + 0.293145i \(0.905298\pi\)
\(812\) 3.70709 + 0.993312i 0.130093 + 0.0348584i
\(813\) −9.37136 2.51105i −0.328668 0.0880663i
\(814\) −36.7209 + 3.09336i −1.28707 + 0.108422i
\(815\) 4.55331 + 7.88656i 0.159495 + 0.276254i
\(816\) 5.58339 9.67071i 0.195458 0.338543i
\(817\) −35.5184 + 9.51712i −1.24263 + 0.332962i
\(818\) 19.8759i 0.694944i
\(819\) 8.02785 + 0.680114i 0.280516 + 0.0237651i
\(820\) 4.12696i 0.144120i
\(821\) −4.35064 + 1.16575i −0.151838 + 0.0406850i −0.333938 0.942595i \(-0.608377\pi\)
0.182099 + 0.983280i \(0.441711\pi\)
\(822\) −1.70938 0.986909i −0.0596213 0.0344224i
\(823\) −31.7517 + 18.3318i −1.10679 + 0.639008i −0.937997 0.346643i \(-0.887322\pi\)
−0.168797 + 0.985651i \(0.553988\pi\)
\(824\) −7.02528 7.02528i −0.244737 0.244737i
\(825\) 21.7425 + 31.2656i 0.756976 + 1.08853i
\(826\) 0.0584025 0.217961i 0.00203208 0.00758384i
\(827\) −36.6500 + 36.6500i −1.27444 + 1.27444i −0.330714 + 0.943731i \(0.607289\pi\)
−0.943731 + 0.330714i \(0.892711\pi\)
\(828\) −0.765578 1.32602i −0.0266057 0.0460824i
\(829\) 38.8490 + 22.4295i 1.34928 + 0.779008i 0.988148 0.153506i \(-0.0490565\pi\)
0.361133 + 0.932514i \(0.382390\pi\)
\(830\) 31.0314 8.31484i 1.07712 0.288612i
\(831\) −7.26497 −0.252019
\(832\) 30.1621 + 10.8843i 1.04568 + 0.377345i
\(833\) 7.87649i 0.272904i
\(834\) −5.90973 22.0554i −0.204637 0.763717i
\(835\) 78.9317 + 45.5712i 2.73154 + 1.57706i
\(836\) 0.925404 5.15103i 0.0320058 0.178152i
\(837\) −1.66735 + 1.66735i −0.0576321 + 0.0576321i
\(838\) 6.94788 25.9298i 0.240011 0.895731i
\(839\) −12.9503 + 48.3313i −0.447095 + 1.66858i 0.263249 + 0.964728i \(0.415206\pi\)
−0.710344 + 0.703855i \(0.751461\pi\)
\(840\) 19.5949 + 19.5949i 0.676089 + 0.676089i
\(841\) −7.76143 13.4432i −0.267636 0.463558i
\(842\) −20.2189 + 35.0202i −0.696791 + 1.20688i
\(843\) 1.61996 + 6.04578i 0.0557944 + 0.208228i
\(844\) 9.36450 0.322339
\(845\) 52.5510 4.88889i 1.80781 0.168183i
\(846\) 5.80540i 0.199594i
\(847\) 10.2438 + 22.3431i 0.351983 + 0.767719i
\(848\) 7.67604 13.2953i 0.263596 0.456562i
\(849\) −3.67452 6.36445i −0.126109 0.218427i
\(850\) 39.4409 39.4409i 1.35281 1.35281i
\(851\) 28.3763 + 7.60340i 0.972726 + 0.260641i
\(852\) −1.40230 + 5.23344i −0.0480419 + 0.179295i
\(853\) −13.4901 + 13.4901i −0.461892 + 0.461892i −0.899275 0.437383i \(-0.855905\pi\)
0.437383 + 0.899275i \(0.355905\pi\)
\(854\) 5.70985 3.29659i 0.195387 0.112807i
\(855\) 6.84643 11.8584i 0.234143 0.405547i
\(856\) −18.9293 + 5.07210i −0.646991 + 0.173361i
\(857\) 25.1653 0.859630 0.429815 0.902917i \(-0.358579\pi\)
0.429815 + 0.902917i \(0.358579\pi\)
\(858\) 7.39486 + 12.8224i 0.252456 + 0.437748i
\(859\) 43.0641 1.46933 0.734664 0.678431i \(-0.237340\pi\)
0.734664 + 0.678431i \(0.237340\pi\)
\(860\) −20.0026 + 5.35969i −0.682084 + 0.182764i
\(861\) −2.42751 + 4.20458i −0.0827294 + 0.143292i
\(862\) 25.0017 14.4347i 0.851562 0.491649i
\(863\) −12.9602 + 12.9602i −0.441170 + 0.441170i −0.892405 0.451235i \(-0.850984\pi\)
0.451235 + 0.892405i \(0.350984\pi\)
\(864\) 0.669662 2.49921i 0.0227824 0.0850249i
\(865\) −48.1267 12.8955i −1.63636 0.438460i
\(866\) −25.0170 + 25.0170i −0.850112 + 0.850112i
\(867\) −0.799174 1.38421i −0.0271414 0.0470102i
\(868\) −1.23255 + 2.13483i −0.0418354 + 0.0724610i
\(869\) 12.9684 27.5783i 0.439924 0.935530i
\(870\) 18.4484i 0.625458i
\(871\) −37.3629 3.16536i −1.26599 0.107254i
\(872\) −3.18845 −0.107974
\(873\) 1.24223 + 4.63608i 0.0420432 + 0.156907i
\(874\) 6.83147 11.8325i 0.231078 0.400239i
\(875\) 29.4027 + 50.9270i 0.993993 + 1.72165i
\(876\) 4.72996 + 4.72996i 0.159810 + 0.159810i
\(877\) −1.04804 + 3.91135i −0.0353899 + 0.132077i −0.981361 0.192175i \(-0.938446\pi\)
0.945971 + 0.324252i \(0.105113\pi\)
\(878\) 2.38504 8.90109i 0.0804912 0.300397i
\(879\) −6.22647 + 6.22647i −0.210013 + 0.210013i
\(880\) −6.77468 + 37.7095i −0.228374 + 1.27119i
\(881\) −2.60804 1.50575i −0.0878671 0.0507301i 0.455423 0.890275i \(-0.349488\pi\)
−0.543290 + 0.839545i \(0.682821\pi\)
\(882\) −0.642977 2.39962i −0.0216501 0.0807994i
\(883\) 4.53816i 0.152721i −0.997080 0.0763607i \(-0.975670\pi\)
0.997080 0.0763607i \(-0.0243301\pi\)
\(884\) −5.05959 + 4.26925i −0.170172 + 0.143591i
\(885\) −0.331218 −0.0111338
\(886\) −39.2911 + 10.5280i −1.32001 + 0.353696i
\(887\) 7.65478 + 4.41949i 0.257022 + 0.148392i 0.622975 0.782241i \(-0.285924\pi\)
−0.365953 + 0.930633i \(0.619257\pi\)
\(888\) 13.7101 + 23.7467i 0.460082 + 0.796886i
\(889\) −5.24847 + 5.24847i −0.176028 + 0.176028i
\(890\) −21.3279 + 79.5970i −0.714914 + 2.66810i
\(891\) 2.72294 1.89357i 0.0912220 0.0634369i
\(892\) 1.84324 + 1.84324i 0.0617161 + 0.0617161i
\(893\) 13.6993 7.90928i 0.458429 0.264674i
\(894\) −15.8068 9.12609i −0.528660 0.305222i
\(895\) 3.34081 0.895167i 0.111671 0.0299221i
\(896\) 13.0351i 0.435472i
\(897\) −2.08098 11.6150i −0.0694819 0.387814i
\(898\) 17.9003i 0.597340i
\(899\) −8.36152 + 2.24046i −0.278872 + 0.0747236i
\(900\) 2.68602 4.65232i 0.0895339 0.155077i
\(901\) 10.5871 + 18.3374i 0.352708 + 0.610907i
\(902\) −8.88837 + 0.748755i −0.295950 + 0.0249308i
\(903\) −23.5314 6.30523i −0.783077 0.209825i
\(904\) 38.8689 + 10.4149i 1.29276 + 0.346395i
\(905\) −54.6543 54.6543i −1.81677 1.81677i
\(906\) −14.7293 25.5120i −0.489350 0.847579i
\(907\) 50.7157 + 29.2807i 1.68399 + 0.972250i 0.958965 + 0.283525i \(0.0915037\pi\)
0.725022 + 0.688726i \(0.241830\pi\)
\(908\) −0.0614329 0.229271i −0.00203872 0.00760862i
\(909\) −11.9920 −0.397749
\(910\) 17.2112 + 36.6461i 0.570545 + 1.21481i
\(911\) 0.664807 0.0220260 0.0110130 0.999939i \(-0.496494\pi\)
0.0110130 + 0.999939i \(0.496494\pi\)
\(912\) 9.26986 2.48385i 0.306956 0.0822485i
\(913\) −7.18752 19.9475i −0.237872 0.660165i
\(914\) −9.14116 + 5.27765i −0.302363 + 0.174569i
\(915\) −6.84317 6.84317i −0.226228 0.226228i
\(916\) 5.86176 + 1.57065i 0.193678 + 0.0518959i
\(917\) 7.46132 27.8460i 0.246395 0.919557i
\(918\) −3.43494 3.43494i −0.113370 0.113370i
\(919\) 0.389717 0.225003i 0.0128556 0.00742217i −0.493558 0.869713i \(-0.664304\pi\)
0.506414 + 0.862290i \(0.330971\pi\)
\(920\) 20.2935 35.1494i 0.669057 1.15884i
\(921\) −1.22827 4.58398i −0.0404730 0.151047i
\(922\) 41.1518i 1.35526i
\(923\) −23.8554 + 34.2691i −0.785209 + 1.12798i
\(924\) 2.23727 2.64888i 0.0736008 0.0871417i
\(925\) 26.6764 + 99.5576i 0.877114 + 3.27344i
\(926\) 25.9874 + 15.0039i 0.854001 + 0.493057i
\(927\) −2.81669 + 1.62622i −0.0925123 + 0.0534120i
\(928\) 6.71650 6.71650i 0.220480 0.220480i
\(929\) 31.0369 + 8.31631i 1.01829 + 0.272849i 0.729088 0.684420i \(-0.239944\pi\)
0.289199 + 0.957269i \(0.406611\pi\)
\(930\) −11.4458 3.06688i −0.375322 0.100567i
\(931\) −4.78651 + 4.78651i −0.156872 + 0.156872i
\(932\) −11.4694 + 6.62188i −0.375694 + 0.216907i
\(933\) −24.6194 14.2140i −0.806004 0.465346i
\(934\) 2.19229 + 8.18175i 0.0717341 + 0.267715i
\(935\) −40.3704 34.0973i −1.32025 1.11510i
\(936\) 6.29249 9.03939i 0.205676 0.295462i
\(937\) 8.11142i 0.264989i −0.991184 0.132494i \(-0.957701\pi\)
0.991184 0.132494i \(-0.0422986\pi\)
\(938\) −7.44473 27.7841i −0.243079 0.907183i
\(939\) 2.72251 4.71552i 0.0888457 0.153885i
\(940\) 7.71492 4.45421i 0.251633 0.145280i
\(941\) −24.8192 24.8192i −0.809084 0.809084i 0.175412 0.984495i \(-0.443874\pi\)
−0.984495 + 0.175412i \(0.943874\pi\)
\(942\) 2.48922 9.28991i 0.0811033 0.302682i
\(943\) 6.86853 + 1.84042i 0.223670 + 0.0599322i
\(944\) −0.164147 0.164147i −0.00534254 0.00534254i
\(945\) 7.85633 4.53586i 0.255567 0.147551i
\(946\) −15.1724 42.1079i −0.493298 1.36905i
\(947\) −3.78617 + 1.01450i −0.123034 + 0.0329669i −0.319811 0.947481i \(-0.603619\pi\)
0.196777 + 0.980448i \(0.436953\pi\)
\(948\) −4.29894 −0.139623
\(949\) 21.9146 + 46.6606i 0.711377 + 1.51467i
\(950\) 47.9362 1.55526
\(951\) 5.67417 + 21.1763i 0.183998 + 0.686689i
\(952\) −23.1987 13.3938i −0.751875 0.434095i
\(953\) −12.6958 21.9898i −0.411258 0.712319i 0.583770 0.811919i \(-0.301577\pi\)
−0.995028 + 0.0996001i \(0.968244\pi\)
\(954\) −4.72235 4.72235i −0.152892 0.152892i
\(955\) −11.0529 2.96162i −0.357664 0.0958358i
\(956\) −8.82545 2.36477i −0.285435 0.0764822i
\(957\) 12.1328 1.02206i 0.392196 0.0330386i
\(958\) −7.38675 12.7942i −0.238655 0.413363i
\(959\) −1.78159 + 3.08580i −0.0575305 + 0.0996457i
\(960\) 34.8757 9.34492i 1.12561 0.301606i
\(961\) 25.4399i 0.820641i
\(962\) 7.06499 + 39.4333i 0.227784 + 1.27138i
\(963\) 6.41537i 0.206732i
\(964\) −0.694435 + 0.186073i −0.0223662 + 0.00599302i
\(965\) 45.4291 + 26.2285i 1.46241 + 0.844325i
\(966\) 7.83917 4.52595i 0.252221 0.145620i
\(967\) −24.2573 24.2573i −0.780062 0.780062i 0.199779 0.979841i \(-0.435978\pi\)
−0.979841 + 0.199779i \(0.935978\pi\)
\(968\) 33.4543 + 3.14443i 1.07526 + 0.101066i
\(969\) −3.42582 + 12.7853i −0.110053 + 0.410725i
\(970\) −17.0550 + 17.0550i −0.547602 + 0.547602i
\(971\) 4.44830 + 7.70469i 0.142753 + 0.247255i 0.928532 0.371252i \(-0.121071\pi\)
−0.785779 + 0.618507i \(0.787738\pi\)
\(972\) −0.405173 0.233927i −0.0129959 0.00750321i
\(973\) −39.8149 + 10.6684i −1.27641 + 0.342012i
\(974\) −16.0127 −0.513081
\(975\) 31.6409 26.6985i 1.01332 0.855035i
\(976\) 6.78278i 0.217112i
\(977\) −11.1604 41.6511i −0.357052 1.33254i −0.877882 0.478877i \(-0.841044\pi\)
0.520830 0.853660i \(-0.325623\pi\)
\(978\) 2.40452 + 1.38825i 0.0768882 + 0.0443914i
\(979\) 53.5294 + 9.61679i 1.71081 + 0.307354i
\(980\) −2.69558 + 2.69558i −0.0861073 + 0.0861073i
\(981\) −0.270151 + 1.00822i −0.00862525 + 0.0321899i
\(982\) 5.28170 19.7116i 0.168546 0.629021i
\(983\) −18.7409 18.7409i −0.597741 0.597741i 0.341970 0.939711i \(-0.388906\pi\)
−0.939711 + 0.341970i \(0.888906\pi\)
\(984\) 3.31857 + 5.74793i 0.105792 + 0.183237i
\(985\) 26.1458 45.2858i 0.833073 1.44292i
\(986\) −4.61561 17.2257i −0.146991 0.548577i
\(987\) 10.4800 0.333583
\(988\) −5.66910 0.480282i −0.180358 0.0152798i
\(989\) 35.6807i 1.13458i
\(990\) 15.0826 + 7.09242i 0.479355 + 0.225412i
\(991\) −15.2742 + 26.4557i −0.485202 + 0.840394i −0.999855 0.0170041i \(-0.994587\pi\)
0.514654 + 0.857398i \(0.327921\pi\)
\(992\) 3.05051 + 5.28363i 0.0968537 + 0.167755i
\(993\) 13.6383 13.6383i 0.432798 0.432798i
\(994\) −30.9391 8.29010i −0.981328 0.262946i
\(995\) 19.0713 71.1752i 0.604602 2.25640i
\(996\) −2.11492 + 2.11492i −0.0670138 + 0.0670138i
\(997\) 34.0232 19.6433i 1.07753 0.622110i 0.147298 0.989092i \(-0.452943\pi\)
0.930228 + 0.366983i \(0.119609\pi\)
\(998\) −3.63189 + 6.29062i −0.114965 + 0.199126i
\(999\) 8.67054 2.32326i 0.274324 0.0735048i
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 429.2.bd.b.175.5 yes 56
11.10 odd 2 inner 429.2.bd.b.175.10 yes 56
13.11 odd 12 inner 429.2.bd.b.76.10 yes 56
143.76 even 12 inner 429.2.bd.b.76.5 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bd.b.76.5 56 143.76 even 12 inner
429.2.bd.b.76.10 yes 56 13.11 odd 12 inner
429.2.bd.b.175.5 yes 56 1.1 even 1 trivial
429.2.bd.b.175.10 yes 56 11.10 odd 2 inner