Properties

Label 847.2.f.z.323.4
Level $847$
Weight $2$
Character 847.323
Analytic conductor $6.763$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 323.4
Character \(\chi\) \(=\) 847.323
Dual form 847.2.f.z.729.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.03276 + 0.750346i) q^{2} +(-0.796038 + 2.44995i) q^{3} +(-0.114455 - 0.352256i) q^{4} +(3.31004 - 2.40489i) q^{5} +(-2.66043 + 1.93292i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.935069 - 2.87785i) q^{8} +(-2.94155 - 2.13716i) q^{9} +O(q^{10})\) \(q+(1.03276 + 0.750346i) q^{2} +(-0.796038 + 2.44995i) q^{3} +(-0.114455 - 0.352256i) q^{4} +(3.31004 - 2.40489i) q^{5} +(-2.66043 + 1.93292i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.935069 - 2.87785i) q^{8} +(-2.94155 - 2.13716i) q^{9} +5.22298 q^{10} +0.954122 q^{12} +(-3.55232 - 2.58091i) q^{13} +(0.394480 - 1.21408i) q^{14} +(3.25694 + 10.0238i) q^{15} +(2.52579 - 1.83509i) q^{16} +(3.39096 - 2.46368i) q^{17} +(-1.43431 - 4.41435i) q^{18} +(0.385900 - 1.18768i) q^{19} +(-1.22599 - 0.890732i) q^{20} +2.57603 q^{21} +4.97180 q^{23} +(6.30624 + 4.58175i) q^{24} +(3.62782 - 11.1653i) q^{25} +(-1.73213 - 5.33093i) q^{26} +(1.32536 - 0.962928i) q^{27} +(-0.299647 + 0.217706i) q^{28} +(0.598078 + 1.84069i) q^{29} +(-4.15769 + 12.7961i) q^{30} +(1.26432 + 0.918580i) q^{31} -2.06640 q^{32} +5.35067 q^{34} +(-3.31004 - 2.40489i) q^{35} +(-0.416153 + 1.28079i) q^{36} +(-0.221348 - 0.681238i) q^{37} +(1.28971 - 0.937030i) q^{38} +(9.15089 - 6.64851i) q^{39} +(-3.82578 - 11.7745i) q^{40} +(-1.48522 + 4.57102i) q^{41} +(2.66043 + 1.93292i) q^{42} -1.35362 q^{43} -14.8763 q^{45} +(5.13469 + 3.73057i) q^{46} +(-3.23424 + 9.95395i) q^{47} +(2.48527 + 7.64887i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(12.1245 - 8.80895i) q^{50} +(3.33656 + 10.2689i) q^{51} +(-0.502561 + 1.54672i) q^{52} +(3.21325 + 2.33457i) q^{53} +2.09131 q^{54} -3.02595 q^{56} +(2.60256 + 1.89087i) q^{57} +(-0.763485 + 2.34976i) q^{58} +(4.25172 + 13.0854i) q^{59} +(3.15818 - 2.29456i) q^{60} +(-9.48745 + 6.89304i) q^{61} +(0.616486 + 1.89735i) q^{62} +(-1.12357 + 3.45799i) q^{63} +(-7.18568 - 5.22070i) q^{64} -17.9651 q^{65} +7.59274 q^{67} +(-1.25596 - 0.912508i) q^{68} +(-3.95774 + 12.1807i) q^{69} +(-1.61399 - 4.96735i) q^{70} +(-0.176622 + 0.128323i) q^{71} +(-8.90096 + 6.46693i) q^{72} +(-3.39036 - 10.4344i) q^{73} +(0.282564 - 0.869644i) q^{74} +(24.4665 + 17.7760i) q^{75} -0.462535 q^{76} +14.4394 q^{78} +(-3.69112 - 2.68176i) q^{79} +(3.94728 - 12.1485i) q^{80} +(-2.06662 - 6.36039i) q^{81} +(-4.96372 + 3.60635i) q^{82} +(1.98579 - 1.44276i) q^{83} +(-0.294840 - 0.907424i) q^{84} +(5.29936 - 16.3098i) q^{85} +(-1.39796 - 1.01568i) q^{86} -4.98571 q^{87} +4.20456 q^{89} +(-15.3636 - 11.1623i) q^{90} +(-1.35686 + 4.17600i) q^{91} +(-0.569047 - 1.75135i) q^{92} +(-3.25692 + 2.36629i) q^{93} +(-10.8091 + 7.85327i) q^{94} +(-1.57889 - 4.85931i) q^{95} +(1.64493 - 5.06259i) q^{96} +(8.83842 + 6.42149i) q^{97} -1.27656 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03276 + 0.750346i 0.730273 + 0.530574i 0.889650 0.456643i \(-0.150948\pi\)
−0.159377 + 0.987218i \(0.550948\pi\)
\(3\) −0.796038 + 2.44995i −0.459593 + 1.41448i 0.406064 + 0.913844i \(0.366901\pi\)
−0.865657 + 0.500637i \(0.833099\pi\)
\(4\) −0.114455 0.352256i −0.0572275 0.176128i
\(5\) 3.31004 2.40489i 1.48030 1.07550i 0.502835 0.864382i \(-0.332290\pi\)
0.977461 0.211115i \(-0.0677096\pi\)
\(6\) −2.66043 + 1.93292i −1.08612 + 0.789109i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) 0.935069 2.87785i 0.330597 1.01747i
\(9\) −2.94155 2.13716i −0.980515 0.712386i
\(10\) 5.22298 1.65165
\(11\) 0 0
\(12\) 0.954122 0.275431
\(13\) −3.55232 2.58091i −0.985236 0.715816i −0.0263633 0.999652i \(-0.508393\pi\)
−0.958873 + 0.283837i \(0.908393\pi\)
\(14\) 0.394480 1.21408i 0.105429 0.324478i
\(15\) 3.25694 + 10.0238i 0.840938 + 2.58814i
\(16\) 2.52579 1.83509i 0.631447 0.458773i
\(17\) 3.39096 2.46368i 0.822429 0.597530i −0.0949779 0.995479i \(-0.530278\pi\)
0.917407 + 0.397949i \(0.130278\pi\)
\(18\) −1.43431 4.41435i −0.338070 1.04047i
\(19\) 0.385900 1.18768i 0.0885315 0.272472i −0.896982 0.442066i \(-0.854246\pi\)
0.985514 + 0.169594i \(0.0542457\pi\)
\(20\) −1.22599 0.890732i −0.274139 0.199174i
\(21\) 2.57603 0.562137
\(22\) 0 0
\(23\) 4.97180 1.03669 0.518346 0.855171i \(-0.326548\pi\)
0.518346 + 0.855171i \(0.326548\pi\)
\(24\) 6.30624 + 4.58175i 1.28726 + 0.935246i
\(25\) 3.62782 11.1653i 0.725563 2.23305i
\(26\) −1.73213 5.33093i −0.339698 1.04548i
\(27\) 1.32536 0.962928i 0.255065 0.185316i
\(28\) −0.299647 + 0.217706i −0.0566280 + 0.0411426i
\(29\) 0.598078 + 1.84069i 0.111060 + 0.341808i 0.991105 0.133083i \(-0.0424875\pi\)
−0.880045 + 0.474891i \(0.842488\pi\)
\(30\) −4.15769 + 12.7961i −0.759088 + 2.33623i
\(31\) 1.26432 + 0.918580i 0.227078 + 0.164982i 0.695507 0.718519i \(-0.255180\pi\)
−0.468429 + 0.883501i \(0.655180\pi\)
\(32\) −2.06640 −0.365292
\(33\) 0 0
\(34\) 5.35067 0.917632
\(35\) −3.31004 2.40489i −0.559499 0.406500i
\(36\) −0.416153 + 1.28079i −0.0693588 + 0.213464i
\(37\) −0.221348 0.681238i −0.0363893 0.111995i 0.931212 0.364478i \(-0.118753\pi\)
−0.967601 + 0.252483i \(0.918753\pi\)
\(38\) 1.28971 0.937030i 0.209219 0.152006i
\(39\) 9.15089 6.64851i 1.46532 1.06461i
\(40\) −3.82578 11.7745i −0.604908 1.86172i
\(41\) −1.48522 + 4.57102i −0.231952 + 0.713874i 0.765559 + 0.643365i \(0.222462\pi\)
−0.997511 + 0.0705088i \(0.977538\pi\)
\(42\) 2.66043 + 1.93292i 0.410513 + 0.298255i
\(43\) −1.35362 −0.206424 −0.103212 0.994659i \(-0.532912\pi\)
−0.103212 + 0.994659i \(0.532912\pi\)
\(44\) 0 0
\(45\) −14.8763 −2.21762
\(46\) 5.13469 + 3.73057i 0.757068 + 0.550042i
\(47\) −3.23424 + 9.95395i −0.471762 + 1.45193i 0.378514 + 0.925596i \(0.376435\pi\)
−0.850276 + 0.526338i \(0.823565\pi\)
\(48\) 2.48527 + 7.64887i 0.358718 + 1.10402i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 12.1245 8.80895i 1.71466 1.24577i
\(51\) 3.33656 + 10.2689i 0.467212 + 1.43793i
\(52\) −0.502561 + 1.54672i −0.0696927 + 0.214492i
\(53\) 3.21325 + 2.33457i 0.441374 + 0.320677i 0.786181 0.617997i \(-0.212055\pi\)
−0.344806 + 0.938674i \(0.612055\pi\)
\(54\) 2.09131 0.284591
\(55\) 0 0
\(56\) −3.02595 −0.404359
\(57\) 2.60256 + 1.89087i 0.344718 + 0.250452i
\(58\) −0.763485 + 2.34976i −0.100250 + 0.308539i
\(59\) 4.25172 + 13.0854i 0.553526 + 1.70358i 0.699804 + 0.714335i \(0.253271\pi\)
−0.146277 + 0.989244i \(0.546729\pi\)
\(60\) 3.15818 2.29456i 0.407720 0.296226i
\(61\) −9.48745 + 6.89304i −1.21474 + 0.882563i −0.995653 0.0931414i \(-0.970309\pi\)
−0.219091 + 0.975704i \(0.570309\pi\)
\(62\) 0.616486 + 1.89735i 0.0782938 + 0.240964i
\(63\) −1.12357 + 3.45799i −0.141557 + 0.435666i
\(64\) −7.18568 5.22070i −0.898210 0.652588i
\(65\) −17.9651 −2.22830
\(66\) 0 0
\(67\) 7.59274 0.927600 0.463800 0.885940i \(-0.346486\pi\)
0.463800 + 0.885940i \(0.346486\pi\)
\(68\) −1.25596 0.912508i −0.152307 0.110658i
\(69\) −3.95774 + 12.1807i −0.476456 + 1.46638i
\(70\) −1.61399 4.96735i −0.192909 0.593712i
\(71\) −0.176622 + 0.128323i −0.0209611 + 0.0152292i −0.598216 0.801335i \(-0.704124\pi\)
0.577255 + 0.816564i \(0.304124\pi\)
\(72\) −8.90096 + 6.46693i −1.04899 + 0.762135i
\(73\) −3.39036 10.4344i −0.396811 1.22126i −0.927542 0.373719i \(-0.878082\pi\)
0.530730 0.847541i \(-0.321918\pi\)
\(74\) 0.282564 0.869644i 0.0328475 0.101094i
\(75\) 24.4665 + 17.7760i 2.82515 + 2.05259i
\(76\) −0.462535 −0.0530564
\(77\) 0 0
\(78\) 14.4394 1.63494
\(79\) −3.69112 2.68176i −0.415284 0.301721i 0.360454 0.932777i \(-0.382622\pi\)
−0.775737 + 0.631056i \(0.782622\pi\)
\(80\) 3.94728 12.1485i 0.441319 1.35824i
\(81\) −2.06662 6.36039i −0.229624 0.706710i
\(82\) −4.96372 + 3.60635i −0.548151 + 0.398255i
\(83\) 1.98579 1.44276i 0.217969 0.158364i −0.473443 0.880825i \(-0.656989\pi\)
0.691412 + 0.722461i \(0.256989\pi\)
\(84\) −0.294840 0.907424i −0.0321697 0.0990081i
\(85\) 5.29936 16.3098i 0.574797 1.76904i
\(86\) −1.39796 1.01568i −0.150746 0.109524i
\(87\) −4.98571 −0.534524
\(88\) 0 0
\(89\) 4.20456 0.445683 0.222841 0.974855i \(-0.428467\pi\)
0.222841 + 0.974855i \(0.428467\pi\)
\(90\) −15.3636 11.1623i −1.61947 1.17661i
\(91\) −1.35686 + 4.17600i −0.142238 + 0.437764i
\(92\) −0.569047 1.75135i −0.0593273 0.182591i
\(93\) −3.25692 + 2.36629i −0.337727 + 0.245373i
\(94\) −10.8091 + 7.85327i −1.11487 + 0.810003i
\(95\) −1.57889 4.85931i −0.161990 0.498555i
\(96\) 1.64493 5.06259i 0.167885 0.516698i
\(97\) 8.83842 + 6.42149i 0.897405 + 0.652003i 0.937798 0.347181i \(-0.112861\pi\)
−0.0403929 + 0.999184i \(0.512861\pi\)
\(98\) −1.27656 −0.128952
\(99\) 0 0
\(100\) −4.34826 −0.434826
\(101\) 5.95905 + 4.32950i 0.592948 + 0.430802i 0.843369 0.537335i \(-0.180569\pi\)
−0.250421 + 0.968137i \(0.580569\pi\)
\(102\) −4.25934 + 13.1089i −0.421737 + 1.29797i
\(103\) −0.0475535 0.146354i −0.00468558 0.0144207i 0.948686 0.316218i \(-0.102413\pi\)
−0.953372 + 0.301798i \(0.902413\pi\)
\(104\) −10.7491 + 7.80970i −1.05404 + 0.765804i
\(105\) 8.52678 6.19507i 0.832129 0.604577i
\(106\) 1.56680 + 4.82210i 0.152181 + 0.468364i
\(107\) −2.45550 + 7.55725i −0.237382 + 0.730587i 0.759414 + 0.650607i \(0.225486\pi\)
−0.996796 + 0.0799799i \(0.974514\pi\)
\(108\) −0.490891 0.356653i −0.0472360 0.0343190i
\(109\) 4.91440 0.470714 0.235357 0.971909i \(-0.424374\pi\)
0.235357 + 0.971909i \(0.424374\pi\)
\(110\) 0 0
\(111\) 1.84520 0.175139
\(112\) −2.52579 1.83509i −0.238665 0.173400i
\(113\) 0.940056 2.89319i 0.0884330 0.272169i −0.897054 0.441922i \(-0.854297\pi\)
0.985487 + 0.169753i \(0.0542969\pi\)
\(114\) 1.26902 + 3.90565i 0.118855 + 0.365797i
\(115\) 16.4569 11.9566i 1.53461 1.11496i
\(116\) 0.579943 0.421353i 0.0538464 0.0391217i
\(117\) 4.93349 + 15.1837i 0.456102 + 1.40374i
\(118\) −5.42759 + 16.7044i −0.499650 + 1.53776i
\(119\) −3.39096 2.46368i −0.310849 0.225845i
\(120\) 31.8925 2.91138
\(121\) 0 0
\(122\) −14.9704 −1.35536
\(123\) −10.0165 7.27742i −0.903158 0.656183i
\(124\) 0.178868 0.550500i 0.0160628 0.0494363i
\(125\) −8.52137 26.2261i −0.762174 2.34573i
\(126\) −3.75507 + 2.72822i −0.334528 + 0.243049i
\(127\) −8.73362 + 6.34535i −0.774984 + 0.563059i −0.903469 0.428653i \(-0.858988\pi\)
0.128486 + 0.991711i \(0.458988\pi\)
\(128\) −2.22666 6.85296i −0.196811 0.605721i
\(129\) 1.07753 3.31630i 0.0948712 0.291984i
\(130\) −18.5537 13.4800i −1.62727 1.18228i
\(131\) 8.70429 0.760497 0.380249 0.924884i \(-0.375838\pi\)
0.380249 + 0.924884i \(0.375838\pi\)
\(132\) 0 0
\(133\) −1.24880 −0.108285
\(134\) 7.84149 + 5.69718i 0.677401 + 0.492161i
\(135\) 2.07125 6.37466i 0.178265 0.548644i
\(136\) −3.91931 12.0624i −0.336078 1.03434i
\(137\) −9.70634 + 7.05207i −0.829269 + 0.602499i −0.919352 0.393435i \(-0.871287\pi\)
0.0900835 + 0.995934i \(0.471287\pi\)
\(138\) −13.2271 + 9.61007i −1.12597 + 0.818064i
\(139\) −2.53075 7.78884i −0.214655 0.660641i −0.999178 0.0405407i \(-0.987092\pi\)
0.784523 0.620100i \(-0.212908\pi\)
\(140\) −0.468285 + 1.44123i −0.0395773 + 0.121807i
\(141\) −21.8122 15.8475i −1.83691 1.33460i
\(142\) −0.278695 −0.0233875
\(143\) 0 0
\(144\) −11.3516 −0.945968
\(145\) 6.40632 + 4.65447i 0.532016 + 0.386532i
\(146\) 4.32801 13.3202i 0.358189 1.10239i
\(147\) −0.796038 2.44995i −0.0656561 0.202069i
\(148\) −0.214636 + 0.155942i −0.0176430 + 0.0128184i
\(149\) 9.77425 7.10141i 0.800738 0.581770i −0.110393 0.993888i \(-0.535211\pi\)
0.911130 + 0.412118i \(0.135211\pi\)
\(150\) 11.9300 + 36.7167i 0.974078 + 2.99790i
\(151\) 2.14720 6.60842i 0.174737 0.537785i −0.824884 0.565302i \(-0.808760\pi\)
0.999621 + 0.0275162i \(0.00875980\pi\)
\(152\) −3.05711 2.22112i −0.247965 0.180157i
\(153\) −15.2399 −1.23208
\(154\) 0 0
\(155\) 6.39402 0.513580
\(156\) −3.38935 2.46250i −0.271365 0.197158i
\(157\) 3.24253 9.97947i 0.258782 0.796449i −0.734279 0.678848i \(-0.762480\pi\)
0.993061 0.117601i \(-0.0375203\pi\)
\(158\) −1.79981 5.53923i −0.143185 0.440678i
\(159\) −8.27745 + 6.01392i −0.656445 + 0.476935i
\(160\) −6.83988 + 4.96946i −0.540740 + 0.392870i
\(161\) −1.53637 4.72846i −0.121083 0.372655i
\(162\) 2.63817 8.11945i 0.207274 0.637924i
\(163\) 6.32444 + 4.59497i 0.495368 + 0.359906i 0.807245 0.590217i \(-0.200958\pi\)
−0.311877 + 0.950123i \(0.600958\pi\)
\(164\) 1.78016 0.139007
\(165\) 0 0
\(166\) 3.13342 0.243201
\(167\) 17.2728 + 12.5494i 1.33661 + 0.971101i 0.999561 + 0.0296124i \(0.00942730\pi\)
0.337045 + 0.941489i \(0.390573\pi\)
\(168\) 2.40877 7.41343i 0.185841 0.571959i
\(169\) 1.94065 + 5.97270i 0.149281 + 0.459438i
\(170\) 17.7109 12.8678i 1.35837 0.986912i
\(171\) −3.67340 + 2.66888i −0.280912 + 0.204094i
\(172\) 0.154928 + 0.476820i 0.0118132 + 0.0363572i
\(173\) −6.00679 + 18.4870i −0.456688 + 1.40554i 0.412455 + 0.910978i \(0.364671\pi\)
−0.869142 + 0.494562i \(0.835329\pi\)
\(174\) −5.14905 3.74100i −0.390349 0.283605i
\(175\) −11.7399 −0.887450
\(176\) 0 0
\(177\) −35.4432 −2.66408
\(178\) 4.34231 + 3.15488i 0.325470 + 0.236468i
\(179\) 5.56120 17.1156i 0.415663 1.27928i −0.495993 0.868327i \(-0.665196\pi\)
0.911656 0.410954i \(-0.134804\pi\)
\(180\) 1.70266 + 5.24026i 0.126909 + 0.390586i
\(181\) −12.2627 + 8.90938i −0.911480 + 0.662229i −0.941389 0.337324i \(-0.890478\pi\)
0.0299086 + 0.999553i \(0.490478\pi\)
\(182\) −4.53476 + 3.29470i −0.336139 + 0.244219i
\(183\) −9.33525 28.7309i −0.690081 2.12385i
\(184\) 4.64898 14.3081i 0.342727 1.05481i
\(185\) −2.37097 1.72261i −0.174317 0.126649i
\(186\) −5.13916 −0.376822
\(187\) 0 0
\(188\) 3.87652 0.282724
\(189\) −1.32536 0.962928i −0.0964055 0.0700427i
\(190\) 2.01555 6.20322i 0.146223 0.450029i
\(191\) −7.34144 22.5946i −0.531208 1.63489i −0.751703 0.659502i \(-0.770767\pi\)
0.220495 0.975388i \(-0.429233\pi\)
\(192\) 18.5106 13.4487i 1.33588 0.970577i
\(193\) 11.3733 8.26319i 0.818668 0.594797i −0.0976625 0.995220i \(-0.531137\pi\)
0.916331 + 0.400422i \(0.131137\pi\)
\(194\) 4.30965 + 13.2637i 0.309415 + 0.952281i
\(195\) 14.3009 44.0137i 1.02411 3.15189i
\(196\) 0.299647 + 0.217706i 0.0214034 + 0.0155505i
\(197\) −18.0665 −1.28718 −0.643591 0.765369i \(-0.722556\pi\)
−0.643591 + 0.765369i \(0.722556\pi\)
\(198\) 0 0
\(199\) 1.54374 0.109433 0.0547163 0.998502i \(-0.482575\pi\)
0.0547163 + 0.998502i \(0.482575\pi\)
\(200\) −28.7397 20.8806i −2.03220 1.47648i
\(201\) −6.04411 + 18.6019i −0.426319 + 1.31207i
\(202\) 2.90566 + 8.94270i 0.204441 + 0.629206i
\(203\) 1.56579 1.13761i 0.109897 0.0798447i
\(204\) 3.23539 2.35065i 0.226523 0.164578i
\(205\) 6.07667 + 18.7021i 0.424413 + 1.30621i
\(206\) 0.0607050 0.186831i 0.00422952 0.0130171i
\(207\) −14.6248 10.6255i −1.01649 0.738525i
\(208\) −13.7086 −0.950522
\(209\) 0 0
\(210\) 13.4546 0.928454
\(211\) −17.8660 12.9804i −1.22995 0.893608i −0.233060 0.972462i \(-0.574874\pi\)
−0.996886 + 0.0788540i \(0.974874\pi\)
\(212\) 0.454592 1.39909i 0.0312215 0.0960900i
\(213\) −0.173788 0.534865i −0.0119078 0.0366483i
\(214\) −8.20650 + 5.96237i −0.560985 + 0.407579i
\(215\) −4.48053 + 3.25529i −0.305569 + 0.222009i
\(216\) −1.53186 4.71458i −0.104230 0.320786i
\(217\) 0.482926 1.48629i 0.0327832 0.100896i
\(218\) 5.07540 + 3.68750i 0.343750 + 0.249749i
\(219\) 28.2628 1.90982
\(220\) 0 0
\(221\) −18.4043 −1.23801
\(222\) 1.90566 + 1.38454i 0.127899 + 0.0929242i
\(223\) −2.64955 + 8.15449i −0.177427 + 0.546065i −0.999736 0.0229766i \(-0.992686\pi\)
0.822309 + 0.569042i \(0.192686\pi\)
\(224\) 0.638553 + 1.96526i 0.0426651 + 0.131310i
\(225\) −34.5333 + 25.0899i −2.30222 + 1.67266i
\(226\) 3.14175 2.28261i 0.208986 0.151837i
\(227\) 8.21085 + 25.2704i 0.544974 + 1.67726i 0.721053 + 0.692880i \(0.243659\pi\)
−0.176079 + 0.984376i \(0.556341\pi\)
\(228\) 0.368196 1.13319i 0.0243844 0.0750473i
\(229\) −9.23194 6.70740i −0.610064 0.443237i 0.239373 0.970928i \(-0.423058\pi\)
−0.849437 + 0.527690i \(0.823058\pi\)
\(230\) 25.9676 1.71225
\(231\) 0 0
\(232\) 5.85648 0.384497
\(233\) 21.5304 + 15.6427i 1.41050 + 1.02479i 0.993249 + 0.115999i \(0.0370069\pi\)
0.417252 + 0.908791i \(0.362993\pi\)
\(234\) −6.29792 + 19.3830i −0.411708 + 1.26711i
\(235\) 13.2327 + 40.7260i 0.863204 + 2.65667i
\(236\) 4.12280 2.99539i 0.268371 0.194983i
\(237\) 9.50845 6.90830i 0.617640 0.448742i
\(238\) −1.65345 5.08879i −0.107177 0.329857i
\(239\) 2.32158 7.14510i 0.150171 0.462178i −0.847469 0.530845i \(-0.821875\pi\)
0.997640 + 0.0686671i \(0.0218746\pi\)
\(240\) 26.6210 + 19.3413i 1.71838 + 1.24848i
\(241\) −27.4388 −1.76749 −0.883744 0.467971i \(-0.844985\pi\)
−0.883744 + 0.467971i \(0.844985\pi\)
\(242\) 0 0
\(243\) 22.1425 1.42044
\(244\) 3.51400 + 2.55307i 0.224961 + 0.163444i
\(245\) −1.26432 + 3.89119i −0.0807747 + 0.248599i
\(246\) −4.88409 15.0317i −0.311398 0.958385i
\(247\) −4.43613 + 3.22304i −0.282264 + 0.205077i
\(248\) 3.82576 2.77957i 0.242936 0.176503i
\(249\) 1.95394 + 6.01360i 0.123826 + 0.381096i
\(250\) 10.8781 33.4793i 0.687990 2.11741i
\(251\) −1.55747 1.13157i −0.0983065 0.0714239i 0.537546 0.843234i \(-0.319351\pi\)
−0.635853 + 0.771810i \(0.719351\pi\)
\(252\) 1.34670 0.0848340
\(253\) 0 0
\(254\) −13.7810 −0.864694
\(255\) 35.7397 + 25.9664i 2.23811 + 1.62608i
\(256\) −2.64690 + 8.14631i −0.165431 + 0.509144i
\(257\) 3.13975 + 9.66315i 0.195852 + 0.602771i 0.999966 + 0.00829511i \(0.00264044\pi\)
−0.804113 + 0.594476i \(0.797360\pi\)
\(258\) 3.60120 2.61643i 0.224201 0.162892i
\(259\) −0.579496 + 0.421028i −0.0360081 + 0.0261614i
\(260\) 2.05620 + 6.32833i 0.127520 + 0.392466i
\(261\) 2.17458 6.69267i 0.134603 0.414266i
\(262\) 8.98946 + 6.53122i 0.555371 + 0.403500i
\(263\) 4.38774 0.270560 0.135280 0.990807i \(-0.456807\pi\)
0.135280 + 0.990807i \(0.456807\pi\)
\(264\) 0 0
\(265\) 16.2504 0.998253
\(266\) −1.28971 0.937030i −0.0790773 0.0574530i
\(267\) −3.34699 + 10.3010i −0.204833 + 0.630410i
\(268\) −0.869027 2.67459i −0.0530842 0.163377i
\(269\) −0.505942 + 0.367588i −0.0308478 + 0.0224123i −0.603102 0.797664i \(-0.706069\pi\)
0.572255 + 0.820076i \(0.306069\pi\)
\(270\) 6.92231 5.02936i 0.421279 0.306077i
\(271\) 3.68889 + 11.3532i 0.224084 + 0.689659i 0.998383 + 0.0568398i \(0.0181024\pi\)
−0.774299 + 0.632819i \(0.781898\pi\)
\(272\) 4.04378 12.4455i 0.245190 0.754617i
\(273\) −9.15089 6.64851i −0.553837 0.402386i
\(274\) −15.3158 −0.925263
\(275\) 0 0
\(276\) 4.74371 0.285538
\(277\) 23.1032 + 16.7854i 1.38814 + 1.00854i 0.996067 + 0.0886037i \(0.0282405\pi\)
0.392069 + 0.919936i \(0.371760\pi\)
\(278\) 3.23066 9.94295i 0.193762 0.596339i
\(279\) −1.75590 5.40409i −0.105123 0.323534i
\(280\) −10.0160 + 7.27706i −0.598571 + 0.434888i
\(281\) 11.8910 8.63932i 0.709357 0.515378i −0.173609 0.984815i \(-0.555543\pi\)
0.882966 + 0.469436i \(0.155543\pi\)
\(282\) −10.6357 32.7333i −0.633346 1.94924i
\(283\) −6.96513 + 21.4365i −0.414034 + 1.27426i 0.499079 + 0.866557i \(0.333672\pi\)
−0.913112 + 0.407708i \(0.866328\pi\)
\(284\) 0.0654178 + 0.0475288i 0.00388183 + 0.00282032i
\(285\) 13.1619 0.779646
\(286\) 0 0
\(287\) 4.80626 0.283704
\(288\) 6.07841 + 4.41623i 0.358174 + 0.260229i
\(289\) 0.175630 0.540533i 0.0103312 0.0317960i
\(290\) 3.12375 + 9.61391i 0.183433 + 0.564548i
\(291\) −22.7681 + 16.5420i −1.33469 + 0.969707i
\(292\) −3.28756 + 2.38855i −0.192390 + 0.139779i
\(293\) −5.20015 16.0044i −0.303796 0.934988i −0.980124 0.198387i \(-0.936430\pi\)
0.676328 0.736601i \(-0.263570\pi\)
\(294\) 1.01619 3.12752i 0.0592656 0.182401i
\(295\) 45.5424 + 33.0885i 2.65158 + 1.92648i
\(296\) −2.16747 −0.125982
\(297\) 0 0
\(298\) 15.4230 0.893429
\(299\) −17.6614 12.8318i −1.02139 0.742081i
\(300\) 3.46138 10.6530i 0.199843 0.615053i
\(301\) 0.418290 + 1.28737i 0.0241099 + 0.0742025i
\(302\) 7.17615 5.21378i 0.412941 0.300019i
\(303\) −15.3507 + 11.1530i −0.881876 + 0.640720i
\(304\) −1.20480 3.70799i −0.0690999 0.212668i
\(305\) −14.8269 + 45.6325i −0.848986 + 2.61291i
\(306\) −15.7392 11.4352i −0.899752 0.653708i
\(307\) −0.238354 −0.0136036 −0.00680179 0.999977i \(-0.502165\pi\)
−0.00680179 + 0.999977i \(0.502165\pi\)
\(308\) 0 0
\(309\) 0.396416 0.0225513
\(310\) 6.60350 + 4.79773i 0.375054 + 0.272493i
\(311\) −0.202877 + 0.624391i −0.0115041 + 0.0354059i −0.956644 0.291260i \(-0.905925\pi\)
0.945140 + 0.326666i \(0.105925\pi\)
\(312\) −10.5767 32.5517i −0.598787 1.84288i
\(313\) 6.02930 4.38054i 0.340796 0.247603i −0.404202 0.914670i \(-0.632451\pi\)
0.744998 + 0.667067i \(0.232451\pi\)
\(314\) 10.8368 7.87340i 0.611557 0.444322i
\(315\) 4.59702 + 14.1482i 0.259013 + 0.797159i
\(316\) −0.522198 + 1.60716i −0.0293759 + 0.0904099i
\(317\) −14.1102 10.2517i −0.792509 0.575791i 0.116198 0.993226i \(-0.462929\pi\)
−0.908707 + 0.417435i \(0.862929\pi\)
\(318\) −13.0612 −0.732433
\(319\) 0 0
\(320\) −36.3401 −2.03147
\(321\) −16.5602 12.0317i −0.924303 0.671545i
\(322\) 1.96128 6.03619i 0.109298 0.336384i
\(323\) −1.61748 4.97811i −0.0899993 0.276989i
\(324\) −2.00395 + 1.45596i −0.111331 + 0.0808865i
\(325\) −41.7037 + 30.2995i −2.31331 + 1.68072i
\(326\) 3.08382 + 9.49103i 0.170797 + 0.525659i
\(327\) −3.91205 + 12.0400i −0.216337 + 0.665816i
\(328\) 11.7659 + 8.54845i 0.649665 + 0.472009i
\(329\) 10.4662 0.577021
\(330\) 0 0
\(331\) −28.6146 −1.57280 −0.786399 0.617719i \(-0.788057\pi\)
−0.786399 + 0.617719i \(0.788057\pi\)
\(332\) −0.735506 0.534377i −0.0403662 0.0293277i
\(333\) −0.804809 + 2.47695i −0.0441033 + 0.135736i
\(334\) 8.42227 + 25.9211i 0.460846 + 1.41834i
\(335\) 25.1323 18.2597i 1.37312 0.997632i
\(336\) 6.50652 4.72726i 0.354960 0.257893i
\(337\) −0.534762 1.64583i −0.0291304 0.0896541i 0.935434 0.353501i \(-0.115009\pi\)
−0.964565 + 0.263847i \(0.915009\pi\)
\(338\) −2.47736 + 7.62453i −0.134751 + 0.414720i
\(339\) 6.33987 + 4.60619i 0.344335 + 0.250174i
\(340\) −6.35176 −0.344472
\(341\) 0 0
\(342\) −5.79633 −0.313430
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) −1.26572 + 3.89550i −0.0682433 + 0.210031i
\(345\) 16.1929 + 49.8365i 0.871794 + 2.68311i
\(346\) −20.0752 + 14.5855i −1.07925 + 0.784121i
\(347\) 2.20869 1.60471i 0.118569 0.0861453i −0.526921 0.849915i \(-0.676653\pi\)
0.645489 + 0.763769i \(0.276653\pi\)
\(348\) 0.570639 + 1.75625i 0.0305895 + 0.0941447i
\(349\) −9.55056 + 29.3936i −0.511230 + 1.57340i 0.278809 + 0.960347i \(0.410060\pi\)
−0.790039 + 0.613057i \(0.789940\pi\)
\(350\) −12.1245 8.80895i −0.648081 0.470858i
\(351\) −7.19332 −0.383951
\(352\) 0 0
\(353\) −23.9543 −1.27496 −0.637480 0.770467i \(-0.720023\pi\)
−0.637480 + 0.770467i \(0.720023\pi\)
\(354\) −36.6044 26.5947i −1.94550 1.41349i
\(355\) −0.276022 + 0.849510i −0.0146498 + 0.0450873i
\(356\) −0.481233 1.48108i −0.0255053 0.0784973i
\(357\) 8.73524 6.34652i 0.462318 0.335894i
\(358\) 18.5860 13.5035i 0.982301 0.713684i
\(359\) 0.468502 + 1.44190i 0.0247266 + 0.0761007i 0.962658 0.270719i \(-0.0872615\pi\)
−0.937932 + 0.346820i \(0.887261\pi\)
\(360\) −13.9103 + 42.8116i −0.733139 + 2.25637i
\(361\) 14.1097 + 10.2513i 0.742614 + 0.539541i
\(362\) −19.3496 −1.01699
\(363\) 0 0
\(364\) 1.62632 0.0852425
\(365\) −36.3159 26.3850i −1.90086 1.38106i
\(366\) 11.9170 36.6769i 0.622914 1.91713i
\(367\) 2.69527 + 8.29518i 0.140692 + 0.433005i 0.996432 0.0844010i \(-0.0268977\pi\)
−0.855740 + 0.517406i \(0.826898\pi\)
\(368\) 12.5577 9.12372i 0.654617 0.475607i
\(369\) 14.1378 10.2717i 0.735986 0.534725i
\(370\) −1.15609 3.55809i −0.0601025 0.184977i
\(371\) 1.22735 3.77741i 0.0637210 0.196113i
\(372\) 1.20631 + 0.876437i 0.0625444 + 0.0454412i
\(373\) 36.8111 1.90601 0.953004 0.302957i \(-0.0979739\pi\)
0.953004 + 0.302957i \(0.0979739\pi\)
\(374\) 0 0
\(375\) 71.0360 3.66828
\(376\) 25.6217 + 18.6153i 1.32134 + 0.960009i
\(377\) 2.62610 8.08232i 0.135251 0.416261i
\(378\) −0.646249 1.98895i −0.0332395 0.102301i
\(379\) −2.10213 + 1.52729i −0.107979 + 0.0784516i −0.640465 0.767988i \(-0.721258\pi\)
0.532485 + 0.846439i \(0.321258\pi\)
\(380\) −1.53101 + 1.11234i −0.0785392 + 0.0570621i
\(381\) −8.59351 26.4481i −0.440259 1.35498i
\(382\) 9.37182 28.8435i 0.479504 1.47576i
\(383\) −15.5649 11.3085i −0.795327 0.577839i 0.114213 0.993456i \(-0.463565\pi\)
−0.909539 + 0.415618i \(0.863565\pi\)
\(384\) 18.5619 0.947235
\(385\) 0 0
\(386\) 17.9462 0.913435
\(387\) 3.98172 + 2.89289i 0.202402 + 0.147054i
\(388\) 1.25041 3.84836i 0.0634798 0.195371i
\(389\) −8.75540 26.9464i −0.443917 1.36623i −0.883668 0.468115i \(-0.844933\pi\)
0.439751 0.898120i \(-0.355067\pi\)
\(390\) 47.7950 34.7251i 2.42019 1.75837i
\(391\) 16.8592 12.2489i 0.852606 0.619455i
\(392\) 0.935069 + 2.87785i 0.0472281 + 0.145353i
\(393\) −6.92895 + 21.3251i −0.349519 + 1.07571i
\(394\) −18.6584 13.5561i −0.939995 0.682946i
\(395\) −18.6671 −0.939243
\(396\) 0 0
\(397\) −10.3666 −0.520287 −0.260143 0.965570i \(-0.583770\pi\)
−0.260143 + 0.965570i \(0.583770\pi\)
\(398\) 1.59431 + 1.15834i 0.0799157 + 0.0580621i
\(399\) 0.994091 3.05950i 0.0497668 0.153167i
\(400\) −11.3262 34.8585i −0.566311 1.74293i
\(401\) 10.3455 7.51648i 0.516632 0.375355i −0.298702 0.954347i \(-0.596554\pi\)
0.815334 + 0.578992i \(0.196554\pi\)
\(402\) −20.1999 + 14.6761i −1.00748 + 0.731978i
\(403\) −2.12048 6.52618i −0.105629 0.325092i
\(404\) 0.843052 2.59465i 0.0419434 0.129089i
\(405\) −22.1366 16.0832i −1.09998 0.799180i
\(406\) 2.47069 0.122618
\(407\) 0 0
\(408\) 32.6722 1.61752
\(409\) −25.9061 18.8219i −1.28098 0.930683i −0.281393 0.959592i \(-0.590797\pi\)
−0.999582 + 0.0289093i \(0.990797\pi\)
\(410\) −7.75725 + 23.8744i −0.383103 + 1.17907i
\(411\) −9.55063 29.3938i −0.471098 1.44989i
\(412\) −0.0461116 + 0.0335020i −0.00227175 + 0.00165053i
\(413\) 11.1311 8.08724i 0.547727 0.397947i
\(414\) −7.13110 21.9473i −0.350475 1.07865i
\(415\) 3.10338 9.55122i 0.152339 0.468851i
\(416\) 7.34052 + 5.33320i 0.359898 + 0.261481i
\(417\) 21.0969 1.03312
\(418\) 0 0
\(419\) −20.0934 −0.981629 −0.490815 0.871264i \(-0.663301\pi\)
−0.490815 + 0.871264i \(0.663301\pi\)
\(420\) −3.15818 2.29456i −0.154104 0.111963i
\(421\) −6.92949 + 21.3268i −0.337722 + 1.03940i 0.627643 + 0.778501i \(0.284020\pi\)
−0.965365 + 0.260902i \(0.915980\pi\)
\(422\) −8.71154 26.8113i −0.424071 1.30516i
\(423\) 30.7868 22.3679i 1.49691 1.08757i
\(424\) 9.72314 7.06427i 0.472197 0.343071i
\(425\) −15.2059 46.7988i −0.737592 2.27008i
\(426\) 0.221852 0.682789i 0.0107487 0.0330812i
\(427\) 9.48745 + 6.89304i 0.459130 + 0.333577i
\(428\) 2.94313 0.142262
\(429\) 0 0
\(430\) −7.06991 −0.340941
\(431\) 9.77748 + 7.10375i 0.470965 + 0.342176i 0.797817 0.602900i \(-0.205988\pi\)
−0.326853 + 0.945075i \(0.605988\pi\)
\(432\) 1.58051 4.86431i 0.0760423 0.234034i
\(433\) −0.0934633 0.287650i −0.00449156 0.0138236i 0.948786 0.315921i \(-0.102313\pi\)
−0.953277 + 0.302097i \(0.902313\pi\)
\(434\) 1.61398 1.17263i 0.0774736 0.0562879i
\(435\) −16.5029 + 11.9901i −0.791254 + 0.574880i
\(436\) −0.562477 1.73113i −0.0269378 0.0829060i
\(437\) 1.91862 5.90490i 0.0917799 0.282470i
\(438\) 29.1887 + 21.2068i 1.39469 + 1.01330i
\(439\) 3.52592 0.168283 0.0841416 0.996454i \(-0.473185\pi\)
0.0841416 + 0.996454i \(0.473185\pi\)
\(440\) 0 0
\(441\) 3.63595 0.173141
\(442\) −19.0073 13.8096i −0.904084 0.656856i
\(443\) −6.75027 + 20.7752i −0.320715 + 0.987059i 0.652623 + 0.757683i \(0.273669\pi\)
−0.973338 + 0.229376i \(0.926331\pi\)
\(444\) −0.211193 0.649984i −0.0100228 0.0308469i
\(445\) 13.9173 10.1115i 0.659743 0.479331i
\(446\) −8.85504 + 6.43357i −0.419298 + 0.304638i
\(447\) 9.61744 + 29.5994i 0.454889 + 1.40001i
\(448\) −2.74469 + 8.44727i −0.129674 + 0.399096i
\(449\) −7.52525 5.46741i −0.355138 0.258023i 0.395883 0.918301i \(-0.370439\pi\)
−0.751022 + 0.660278i \(0.770439\pi\)
\(450\) −54.4908 −2.56872
\(451\) 0 0
\(452\) −1.12674 −0.0529974
\(453\) 14.4811 + 10.5211i 0.680380 + 0.494325i
\(454\) −10.4817 + 32.2593i −0.491930 + 1.51400i
\(455\) 5.55153 + 17.0858i 0.260260 + 0.800997i
\(456\) 7.87522 5.72169i 0.368791 0.267942i
\(457\) −9.15527 + 6.65169i −0.428266 + 0.311153i −0.780955 0.624587i \(-0.785267\pi\)
0.352689 + 0.935740i \(0.385267\pi\)
\(458\) −4.50153 13.8543i −0.210343 0.647369i
\(459\) 2.12189 6.53051i 0.0990414 0.304818i
\(460\) −6.09536 4.42854i −0.284198 0.206482i
\(461\) 0.678821 0.0316158 0.0158079 0.999875i \(-0.494968\pi\)
0.0158079 + 0.999875i \(0.494968\pi\)
\(462\) 0 0
\(463\) −13.4936 −0.627103 −0.313551 0.949571i \(-0.601519\pi\)
−0.313551 + 0.949571i \(0.601519\pi\)
\(464\) 4.88846 + 3.55168i 0.226941 + 0.164882i
\(465\) −5.08989 + 15.6651i −0.236038 + 0.726450i
\(466\) 10.4983 + 32.3104i 0.486324 + 1.49675i
\(467\) −23.9928 + 17.4318i −1.11026 + 0.806649i −0.982704 0.185183i \(-0.940712\pi\)
−0.127552 + 0.991832i \(0.540712\pi\)
\(468\) 4.78390 3.47571i 0.221136 0.160665i
\(469\) −2.34628 7.22112i −0.108341 0.333440i
\(470\) −16.8924 + 51.9893i −0.779186 + 2.39809i
\(471\) 21.8681 + 15.8881i 1.00763 + 0.732084i
\(472\) 41.6335 1.91634
\(473\) 0 0
\(474\) 15.0036 0.689137
\(475\) −11.8608 8.61735i −0.544210 0.395391i
\(476\) −0.479734 + 1.47647i −0.0219886 + 0.0676738i
\(477\) −4.46260 13.7345i −0.204328 0.628858i
\(478\) 7.75893 5.63719i 0.354885 0.257839i
\(479\) 3.80348 2.76339i 0.173785 0.126262i −0.497492 0.867468i \(-0.665746\pi\)
0.671278 + 0.741206i \(0.265746\pi\)
\(480\) −6.73015 20.7133i −0.307188 0.945427i
\(481\) −0.971917 + 2.99125i −0.0443156 + 0.136389i
\(482\) −28.3377 20.5886i −1.29075 0.937784i
\(483\) 12.8075 0.582763
\(484\) 0 0
\(485\) 44.6985 2.02965
\(486\) 22.8679 + 16.6145i 1.03731 + 0.753649i
\(487\) 10.0040 30.7893i 0.453327 1.39520i −0.419762 0.907634i \(-0.637886\pi\)
0.873089 0.487562i \(-0.162114\pi\)
\(488\) 10.9657 + 33.7489i 0.496393 + 1.52774i
\(489\) −16.2920 + 11.8368i −0.736748 + 0.535279i
\(490\) −4.22548 + 3.06999i −0.190888 + 0.138688i
\(491\) 2.11860 + 6.52038i 0.0956111 + 0.294261i 0.987412 0.158166i \(-0.0505582\pi\)
−0.891801 + 0.452427i \(0.850558\pi\)
\(492\) −1.41708 + 4.36131i −0.0638868 + 0.196623i
\(493\) 6.56294 + 4.76826i 0.295580 + 0.214751i
\(494\) −6.99986 −0.314939
\(495\) 0 0
\(496\) 4.87908 0.219077
\(497\) 0.176622 + 0.128323i 0.00792256 + 0.00575608i
\(498\) −2.49432 + 7.67674i −0.111773 + 0.344003i
\(499\) 3.38900 + 10.4303i 0.151713 + 0.466923i 0.997813 0.0661003i \(-0.0210557\pi\)
−0.846100 + 0.533023i \(0.821056\pi\)
\(500\) −8.26298 + 6.00341i −0.369532 + 0.268481i
\(501\) −44.4952 + 32.3277i −1.98790 + 1.44429i
\(502\) −0.759428 2.33728i −0.0338949 0.104318i
\(503\) 8.32288 25.6152i 0.371099 1.14213i −0.574974 0.818172i \(-0.694988\pi\)
0.946073 0.323954i \(-0.105012\pi\)
\(504\) 8.90096 + 6.46693i 0.396480 + 0.288060i
\(505\) 30.1367 1.34106
\(506\) 0 0
\(507\) −16.1777 −0.718475
\(508\) 3.23480 + 2.35022i 0.143521 + 0.104274i
\(509\) 9.39282 28.9081i 0.416330 1.28133i −0.494727 0.869049i \(-0.664732\pi\)
0.911056 0.412282i \(-0.135268\pi\)
\(510\) 17.4268 + 53.6342i 0.771672 + 2.37496i
\(511\) −8.87607 + 6.44884i −0.392654 + 0.285280i
\(512\) −20.5051 + 14.8978i −0.906206 + 0.658397i
\(513\) −0.632193 1.94569i −0.0279120 0.0859043i
\(514\) −4.00809 + 12.3356i −0.176789 + 0.544102i
\(515\) −0.509370 0.370079i −0.0224455 0.0163076i
\(516\) −1.29151 −0.0568558
\(517\) 0 0
\(518\) −0.914398 −0.0401763
\(519\) −40.5106 29.4327i −1.77822 1.29195i
\(520\) −16.7986 + 51.7009i −0.736669 + 2.26723i
\(521\) −0.289063 0.889643i −0.0126641 0.0389760i 0.944525 0.328440i \(-0.106523\pi\)
−0.957189 + 0.289464i \(0.906523\pi\)
\(522\) 7.26764 5.28025i 0.318096 0.231110i
\(523\) 21.1844 15.3913i 0.926328 0.673017i −0.0187630 0.999824i \(-0.505973\pi\)
0.945091 + 0.326807i \(0.105973\pi\)
\(524\) −0.996249 3.06614i −0.0435214 0.133945i
\(525\) 9.34538 28.7621i 0.407866 1.25528i
\(526\) 4.53150 + 3.29232i 0.197583 + 0.143552i
\(527\) 6.55034 0.285337
\(528\) 0 0
\(529\) 1.71881 0.0747307
\(530\) 16.7828 + 12.1934i 0.728997 + 0.529647i
\(531\) 15.4590 47.5780i 0.670865 2.06471i
\(532\) 0.142931 + 0.439897i 0.00619685 + 0.0190720i
\(533\) 17.0734 12.4045i 0.739529 0.537300i
\(534\) −11.1859 + 8.12707i −0.484063 + 0.351693i
\(535\) 10.0465 + 30.9200i 0.434349 + 1.33679i
\(536\) 7.09973 21.8507i 0.306662 0.943808i
\(537\) 37.5055 + 27.2493i 1.61848 + 1.17590i
\(538\) −0.798336 −0.0344187
\(539\) 0 0
\(540\) −2.48258 −0.106833
\(541\) 21.6465 + 15.7271i 0.930656 + 0.676161i 0.946153 0.323719i \(-0.104933\pi\)
−0.0154971 + 0.999880i \(0.504933\pi\)
\(542\) −4.70910 + 14.4931i −0.202273 + 0.622533i
\(543\) −12.0660 37.1353i −0.517801 1.59363i
\(544\) −7.00709 + 5.09095i −0.300427 + 0.218273i
\(545\) 16.2669 11.8186i 0.696796 0.506252i
\(546\) −4.46201 13.7327i −0.190957 0.587704i
\(547\) −14.3563 + 44.1843i −0.613833 + 1.88918i −0.196216 + 0.980561i \(0.562865\pi\)
−0.417617 + 0.908623i \(0.637135\pi\)
\(548\) 3.59508 + 2.61198i 0.153574 + 0.111578i
\(549\) 42.6393 1.81980
\(550\) 0 0
\(551\) 2.41695 0.102966
\(552\) 31.3534 + 22.7796i 1.33449 + 0.969563i
\(553\) −1.40988 + 4.33917i −0.0599543 + 0.184520i
\(554\) 11.2652 + 34.6707i 0.478613 + 1.47302i
\(555\) 6.10770 4.43750i 0.259257 0.188362i
\(556\) −2.45401 + 1.78294i −0.104073 + 0.0756136i
\(557\) −10.8457 33.3796i −0.459546 1.41434i −0.865714 0.500539i \(-0.833135\pi\)
0.406167 0.913799i \(-0.366865\pi\)
\(558\) 2.24151 6.89867i 0.0948908 0.292044i
\(559\) 4.80848 + 3.49356i 0.203377 + 0.147762i
\(560\) −12.7737 −0.539786
\(561\) 0 0
\(562\) 18.7630 0.791471
\(563\) −7.23901 5.25945i −0.305088 0.221659i 0.424698 0.905335i \(-0.360380\pi\)
−0.729786 + 0.683676i \(0.760380\pi\)
\(564\) −3.08586 + 9.49729i −0.129938 + 0.399908i
\(565\) −3.84618 11.8373i −0.161810 0.498000i
\(566\) −23.2781 + 16.9125i −0.978450 + 0.710885i
\(567\) −5.41047 + 3.93094i −0.227219 + 0.165084i
\(568\) 0.204141 + 0.628281i 0.00856556 + 0.0263621i
\(569\) −6.00285 + 18.4749i −0.251653 + 0.774507i 0.742818 + 0.669493i \(0.233489\pi\)
−0.994471 + 0.105014i \(0.966511\pi\)
\(570\) 13.5932 + 9.87600i 0.569354 + 0.413660i
\(571\) −16.0171 −0.670295 −0.335148 0.942166i \(-0.608786\pi\)
−0.335148 + 0.942166i \(0.608786\pi\)
\(572\) 0 0
\(573\) 61.1999 2.55666
\(574\) 4.96372 + 3.60635i 0.207182 + 0.150526i
\(575\) 18.0368 55.5115i 0.752186 2.31499i
\(576\) 9.97954 + 30.7139i 0.415814 + 1.27974i
\(577\) 26.6322 19.3494i 1.10871 0.805526i 0.126251 0.991998i \(-0.459705\pi\)
0.982460 + 0.186472i \(0.0597054\pi\)
\(578\) 0.586970 0.426459i 0.0244147 0.0177383i
\(579\) 11.1908 + 34.4419i 0.465076 + 1.43136i
\(580\) 0.906329 2.78939i 0.0376333 0.115823i
\(581\) −1.98579 1.44276i −0.0823846 0.0598559i
\(582\) −35.9262 −1.48919
\(583\) 0 0
\(584\) −33.1990 −1.37378
\(585\) 52.8452 + 38.3943i 2.18488 + 1.58741i
\(586\) 6.63833 20.4307i 0.274227 0.843983i
\(587\) 8.47857 + 26.0944i 0.349948 + 1.07703i 0.958881 + 0.283808i \(0.0915978\pi\)
−0.608933 + 0.793222i \(0.708402\pi\)
\(588\) −0.771901 + 0.560819i −0.0318327 + 0.0231278i
\(589\) 1.57888 1.14712i 0.0650565 0.0472663i
\(590\) 22.2066 + 68.3450i 0.914233 + 2.81372i
\(591\) 14.3816 44.2620i 0.591580 1.82070i
\(592\) −1.80921 1.31447i −0.0743582 0.0540244i
\(593\) −14.6132 −0.600092 −0.300046 0.953925i \(-0.597002\pi\)
−0.300046 + 0.953925i \(0.597002\pi\)
\(594\) 0 0
\(595\) −17.1491 −0.703045
\(596\) −3.62023 2.63025i −0.148290 0.107739i
\(597\) −1.22887 + 3.78208i −0.0502944 + 0.154790i
\(598\) −8.61178 26.5043i −0.352162 1.08384i
\(599\) −20.4491 + 14.8571i −0.835527 + 0.607046i −0.921118 0.389284i \(-0.872722\pi\)
0.0855904 + 0.996330i \(0.472722\pi\)
\(600\) 74.0344 53.7891i 3.02244 2.19593i
\(601\) 2.87416 + 8.84576i 0.117239 + 0.360826i 0.992408 0.122993i \(-0.0392493\pi\)
−0.875168 + 0.483819i \(0.839249\pi\)
\(602\) −0.533974 + 1.64340i −0.0217632 + 0.0669802i
\(603\) −22.3344 16.2269i −0.909526 0.660810i
\(604\) −2.57361 −0.104719
\(605\) 0 0
\(606\) −24.2222 −0.983960
\(607\) −1.72055 1.25005i −0.0698349 0.0507380i 0.552320 0.833632i \(-0.313743\pi\)
−0.622155 + 0.782894i \(0.713743\pi\)
\(608\) −0.797424 + 2.45422i −0.0323398 + 0.0995317i
\(609\) 1.54067 + 4.74169i 0.0624311 + 0.192143i
\(610\) −49.5528 + 36.0022i −2.00633 + 1.45769i
\(611\) 37.1793 27.0123i 1.50411 1.09280i
\(612\) 1.74429 + 5.36837i 0.0705087 + 0.217003i
\(613\) 12.6526 38.9408i 0.511035 1.57280i −0.279347 0.960190i \(-0.590118\pi\)
0.790382 0.612614i \(-0.209882\pi\)
\(614\) −0.246163 0.178848i −0.00993433 0.00721771i
\(615\) −50.6564 −2.04266
\(616\) 0 0
\(617\) −7.53813 −0.303474 −0.151737 0.988421i \(-0.548487\pi\)
−0.151737 + 0.988421i \(0.548487\pi\)
\(618\) 0.409404 + 0.297449i 0.0164686 + 0.0119652i
\(619\) −6.02754 + 18.5509i −0.242267 + 0.745623i 0.753806 + 0.657097i \(0.228216\pi\)
−0.996074 + 0.0885260i \(0.971784\pi\)
\(620\) −0.731828 2.25233i −0.0293909 0.0904559i
\(621\) 6.58941 4.78749i 0.264424 0.192115i
\(622\) −0.678032 + 0.492619i −0.0271866 + 0.0197522i
\(623\) −1.29928 3.99878i −0.0520546 0.160208i
\(624\) 10.9126 33.5855i 0.436853 1.34450i
\(625\) −43.7881 31.8139i −1.75152 1.27256i
\(626\) 9.51375 0.380246
\(627\) 0 0
\(628\) −3.88645 −0.155086
\(629\) −2.42893 1.76472i −0.0968479 0.0703641i
\(630\) −5.86839 + 18.0610i −0.233802 + 0.719569i
\(631\) −3.29578 10.1434i −0.131203 0.403801i 0.863777 0.503874i \(-0.168092\pi\)
−0.994980 + 0.100073i \(0.968092\pi\)
\(632\) −11.1691 + 8.11485i −0.444284 + 0.322792i
\(633\) 46.0234 33.4380i 1.82927 1.32904i
\(634\) −6.88020 21.1751i −0.273248 0.840970i
\(635\) −13.6488 + 42.0067i −0.541637 + 1.66699i
\(636\) 3.06584 + 2.22746i 0.121568 + 0.0883246i
\(637\) 4.39091 0.173974
\(638\) 0 0
\(639\) 0.793787 0.0314017
\(640\) −23.8509 17.3287i −0.942791 0.684977i
\(641\) 0.138547 0.426405i 0.00547230 0.0168420i −0.948283 0.317426i \(-0.897182\pi\)
0.953755 + 0.300584i \(0.0971815\pi\)
\(642\) −8.07485 24.8518i −0.318689 0.980823i
\(643\) 25.6005 18.5999i 1.00959 0.733507i 0.0454636 0.998966i \(-0.485524\pi\)
0.964122 + 0.265459i \(0.0855235\pi\)
\(644\) −1.48979 + 1.08239i −0.0587058 + 0.0426522i
\(645\) −4.40865 13.5684i −0.173590 0.534256i
\(646\) 2.06482 6.35487i 0.0812394 0.250029i
\(647\) 24.3710 + 17.7065i 0.958122 + 0.696116i 0.952714 0.303869i \(-0.0982786\pi\)
0.00540790 + 0.999985i \(0.498279\pi\)
\(648\) −20.2367 −0.794972
\(649\) 0 0
\(650\) −65.8051 −2.58109
\(651\) 3.25692 + 2.36629i 0.127649 + 0.0927423i
\(652\) 0.894744 2.75374i 0.0350409 0.107845i
\(653\) 10.6954 + 32.9170i 0.418543 + 1.28814i 0.909043 + 0.416702i \(0.136814\pi\)
−0.490500 + 0.871441i \(0.663186\pi\)
\(654\) −13.0744 + 9.49912i −0.511250 + 0.371445i
\(655\) 28.8116 20.9328i 1.12576 0.817913i
\(656\) 4.63691 + 14.2710i 0.181041 + 0.557187i
\(657\) −12.3272 + 37.9391i −0.480929 + 1.48015i
\(658\) 10.8091 + 7.85327i 0.421383 + 0.306152i
\(659\) 20.2587 0.789167 0.394584 0.918860i \(-0.370889\pi\)
0.394584 + 0.918860i \(0.370889\pi\)
\(660\) 0 0
\(661\) 40.6737 1.58202 0.791012 0.611801i \(-0.209555\pi\)
0.791012 + 0.611801i \(0.209555\pi\)
\(662\) −29.5520 21.4708i −1.14857 0.834487i
\(663\) 14.6505 45.0897i 0.568980 1.75114i
\(664\) −2.29520 7.06389i −0.0890710 0.274132i
\(665\) −4.13358 + 3.00322i −0.160293 + 0.116460i
\(666\) −2.68974 + 1.95421i −0.104225 + 0.0757242i
\(667\) 2.97352 + 9.15157i 0.115135 + 0.354350i
\(668\) 2.44365 7.52078i 0.0945476 0.290988i
\(669\) −17.8690 12.9826i −0.690854 0.501935i
\(670\) 39.6567 1.53207
\(671\) 0 0
\(672\) −5.32312 −0.205344
\(673\) 20.0219 + 14.5467i 0.771786 + 0.560735i 0.902503 0.430685i \(-0.141728\pi\)
−0.130717 + 0.991420i \(0.541728\pi\)
\(674\) 0.682659 2.10101i 0.0262950 0.0809278i
\(675\) −5.94320 18.2913i −0.228754 0.704032i
\(676\) 1.88180 1.36721i 0.0723771 0.0525850i
\(677\) −9.20835 + 6.69026i −0.353906 + 0.257128i −0.750506 0.660864i \(-0.770190\pi\)
0.396600 + 0.917992i \(0.370190\pi\)
\(678\) 3.09135 + 9.51419i 0.118723 + 0.365390i
\(679\) 3.37598 10.3902i 0.129558 0.398739i
\(680\) −41.9817 30.5015i −1.60993 1.16968i
\(681\) −68.4475 −2.62291
\(682\) 0 0
\(683\) −0.212700 −0.00813875 −0.00406938 0.999992i \(-0.501295\pi\)
−0.00406938 + 0.999992i \(0.501295\pi\)
\(684\) 1.36057 + 0.988511i 0.0520226 + 0.0377967i
\(685\) −15.1690 + 46.6853i −0.579577 + 1.78375i
\(686\) 0.394480 + 1.21408i 0.0150613 + 0.0463540i
\(687\) 23.7818 17.2785i 0.907332 0.659215i
\(688\) −3.41895 + 2.48401i −0.130346 + 0.0947021i
\(689\) −5.38920 16.5862i −0.205312 0.631886i
\(690\) −20.6712 + 63.6195i −0.786940 + 2.42195i
\(691\) −29.4324 21.3839i −1.11966 0.813481i −0.135503 0.990777i \(-0.543265\pi\)
−0.984158 + 0.177296i \(0.943265\pi\)
\(692\) 7.19966 0.273690
\(693\) 0 0
\(694\) 3.48514 0.132294
\(695\) −27.1082 19.6952i −1.02827 0.747083i
\(696\) −4.66198 + 14.3481i −0.176712 + 0.543864i
\(697\) 6.22522 + 19.1593i 0.235797 + 0.725709i
\(698\) −31.9188 + 23.1904i −1.20814 + 0.877769i
\(699\) −55.4630 + 40.2962i −2.09780 + 1.52414i
\(700\) 1.34369 + 4.13544i 0.0507865 + 0.156305i
\(701\) 5.79080 17.8223i 0.218716 0.673138i −0.780153 0.625588i \(-0.784859\pi\)
0.998869 0.0475491i \(-0.0151411\pi\)
\(702\) −7.42899 5.39748i −0.280389 0.203715i
\(703\) −0.894509 −0.0337371
\(704\) 0 0
\(705\) −110.310 −4.15453
\(706\) −24.7391 17.9740i −0.931068 0.676461i
\(707\) 2.27616 7.00529i 0.0856036 0.263461i
\(708\) 4.05666 + 12.4851i 0.152458 + 0.469219i
\(709\) 10.3227 7.49988i 0.387677 0.281664i −0.376826 0.926284i \(-0.622985\pi\)
0.764503 + 0.644620i \(0.222985\pi\)
\(710\) −0.922491 + 0.670229i −0.0346205 + 0.0251533i
\(711\) 5.12626 + 15.7770i 0.192250 + 0.591684i
\(712\) 3.93156 12.1001i 0.147341 0.453470i
\(713\) 6.28593 + 4.56700i 0.235410 + 0.171035i
\(714\) 13.7835 0.515835
\(715\) 0 0
\(716\) −6.66558 −0.249105
\(717\) 15.6571 + 11.3755i 0.584725 + 0.424827i
\(718\) −0.598073 + 1.84068i −0.0223199 + 0.0686936i
\(719\) −5.29123 16.2847i −0.197329 0.607318i −0.999942 0.0108162i \(-0.996557\pi\)
0.802612 0.596501i \(-0.203443\pi\)
\(720\) −37.5743 + 27.2993i −1.40031 + 1.01739i
\(721\) −0.124497 + 0.0904521i −0.00463649 + 0.00336861i
\(722\) 6.87993 + 21.1742i 0.256044 + 0.788024i
\(723\) 21.8423 67.2238i 0.812325 2.50008i
\(724\) 4.54191 + 3.29989i 0.168799 + 0.122640i
\(725\) 22.7216 0.843858
\(726\) 0 0
\(727\) −8.65786 −0.321102 −0.160551 0.987028i \(-0.551327\pi\)
−0.160551 + 0.987028i \(0.551327\pi\)
\(728\) 10.7491 + 7.80970i 0.398389 + 0.289447i
\(729\) −11.4264 + 35.1668i −0.423200 + 1.30248i
\(730\) −17.7078 54.4989i −0.655394 2.01710i
\(731\) −4.59006 + 3.33488i −0.169770 + 0.123345i
\(732\) −9.05219 + 6.57680i −0.334579 + 0.243086i
\(733\) −8.67924 26.7120i −0.320575 0.986629i −0.973398 0.229119i \(-0.926416\pi\)
0.652823 0.757510i \(-0.273584\pi\)
\(734\) −3.44068 + 10.5893i −0.126998 + 0.390859i
\(735\) −8.52678 6.19507i −0.314515 0.228509i
\(736\) −10.2737 −0.378695
\(737\) 0 0
\(738\) 22.3084 0.821182
\(739\) −27.4228 19.9239i −1.00877 0.732911i −0.0448155 0.998995i \(-0.514270\pi\)
−0.963950 + 0.266084i \(0.914270\pi\)
\(740\) −0.335431 + 1.03235i −0.0123307 + 0.0379500i
\(741\) −4.36496 13.4340i −0.160351 0.493509i
\(742\) 4.10193 2.98022i 0.150586 0.109407i
\(743\) −4.57354 + 3.32287i −0.167787 + 0.121904i −0.668510 0.743703i \(-0.733068\pi\)
0.500723 + 0.865608i \(0.333068\pi\)
\(744\) 3.76438 + 11.5856i 0.138009 + 0.424748i
\(745\) 15.2751 47.0119i 0.559636 1.72238i
\(746\) 38.0171 + 27.6211i 1.39191 + 1.01128i
\(747\) −8.92472 −0.326538
\(748\) 0 0
\(749\) 7.94617 0.290347
\(750\) 73.3633 + 53.3015i 2.67885 + 1.94630i
\(751\) 13.7021 42.1707i 0.499997 1.53883i −0.309025 0.951054i \(-0.600003\pi\)
0.809022 0.587778i \(-0.199997\pi\)
\(752\) 10.0974 + 31.0767i 0.368216 + 1.13325i
\(753\) 4.01209 2.91495i 0.146209 0.106227i
\(754\) 8.77667 6.37663i 0.319628 0.232223i
\(755\) −8.78515 27.0379i −0.319724 0.984011i
\(756\) −0.187504 + 0.577077i −0.00681944 + 0.0209881i
\(757\) 17.2953 + 12.5657i 0.628607 + 0.456710i 0.855917 0.517113i \(-0.172993\pi\)
−0.227311 + 0.973822i \(0.572993\pi\)
\(758\) −3.31700 −0.120479
\(759\) 0 0
\(760\) −15.4607 −0.560819
\(761\) −3.70994 2.69543i −0.134485 0.0977092i 0.518509 0.855072i \(-0.326487\pi\)
−0.652994 + 0.757363i \(0.726487\pi\)
\(762\) 10.9702 33.7627i 0.397407 1.22309i
\(763\) −1.51863 4.67387i −0.0549782 0.169205i
\(764\) −7.11883 + 5.17214i −0.257550 + 0.187121i
\(765\) −50.4449 + 36.6503i −1.82384 + 1.32510i
\(766\) −7.58948 23.3580i −0.274219 0.843960i
\(767\) 18.6689 57.4569i 0.674095 2.07465i
\(768\) −17.8510 12.9695i −0.644144 0.467998i
\(769\) −12.8223 −0.462385 −0.231193 0.972908i \(-0.574263\pi\)
−0.231193 + 0.972908i \(0.574263\pi\)
\(770\) 0 0
\(771\) −26.1736 −0.942621
\(772\) −4.21249 3.06055i −0.151611 0.110152i
\(773\) 16.7067 51.4178i 0.600897 1.84937i 0.0780395 0.996950i \(-0.475134\pi\)
0.522857 0.852420i \(-0.324866\pi\)
\(774\) 1.94150 + 5.97534i 0.0697859 + 0.214779i
\(775\) 14.8429 10.7840i 0.533173 0.387373i
\(776\) 26.7446 19.4311i 0.960075 0.697535i
\(777\) −0.570199 1.75489i −0.0204558 0.0629564i
\(778\) 11.1768 34.3988i 0.400709 1.23326i
\(779\) 4.85576 + 3.52792i 0.173976 + 0.126401i
\(780\) −17.1409 −0.613743
\(781\) 0 0
\(782\) 26.6025 0.951302
\(783\) 2.56512 + 1.86367i 0.0916700 + 0.0666021i
\(784\) −0.964766 + 2.96924i −0.0344559 + 0.106044i
\(785\) −13.2666 40.8304i −0.473505 1.45730i
\(786\) −23.1572 + 16.8247i −0.825988 + 0.600116i
\(787\) −35.4766 + 25.7752i −1.26460 + 0.918788i −0.998974 0.0452876i \(-0.985580\pi\)
−0.265629 + 0.964075i \(0.585580\pi\)
\(788\) 2.06780 + 6.36403i 0.0736622 + 0.226709i
\(789\) −3.49281 + 10.7498i −0.124347 + 0.382702i
\(790\) −19.2787 14.0068i −0.685904 0.498338i
\(791\) −3.04208 −0.108164
\(792\) 0 0
\(793\) 51.4928 1.82856
\(794\) −10.7063 7.77856i −0.379951 0.276051i
\(795\) −12.9359 + 39.8127i −0.458790 + 1.41201i
\(796\) −0.176688 0.543791i −0.00626255 0.0192742i
\(797\) 28.9383 21.0249i 1.02505 0.744740i 0.0577359 0.998332i \(-0.481612\pi\)
0.967311 + 0.253591i \(0.0816119\pi\)
\(798\) 3.32234 2.41382i 0.117610 0.0854484i
\(799\) 13.5562 + 41.7216i 0.479583 + 1.47600i
\(800\) −7.49652 + 23.0719i −0.265042 + 0.815716i
\(801\) −12.3679 8.98582i −0.436999 0.317498i
\(802\) 16.3244 0.576436
\(803\) 0 0
\(804\) 7.24440 0.255490
\(805\) −16.4569 11.9566i −0.580029 0.421415i
\(806\) 2.70693 8.33108i 0.0953477 0.293450i
\(807\) −0.497825 1.53215i −0.0175243 0.0539342i
\(808\) 18.0318 13.1009i 0.634356 0.460886i
\(809\) −24.8424 + 18.0490i −0.873411 + 0.634570i −0.931500 0.363741i \(-0.881499\pi\)
0.0580894 + 0.998311i \(0.481499\pi\)
\(810\) −10.7939 33.2202i −0.379259 1.16724i
\(811\) −5.28368 + 16.2615i −0.185535 + 0.571019i −0.999957 0.00925442i \(-0.997054\pi\)
0.814422 + 0.580273i \(0.197054\pi\)
\(812\) −0.579943 0.421353i −0.0203520 0.0147866i
\(813\) −30.7514 −1.07850
\(814\) 0 0
\(815\) 31.9845 1.12037
\(816\) 27.2718 + 19.8141i 0.954705 + 0.693634i
\(817\) −0.522360 + 1.60766i −0.0182751 + 0.0562449i
\(818\) −12.6319 38.8771i −0.441665 1.35931i
\(819\) 12.9161 9.38406i 0.451324 0.327906i
\(820\) 5.89241 4.28109i 0.205772 0.149502i
\(821\) 3.82631 + 11.7762i 0.133539 + 0.410991i 0.995360 0.0962218i \(-0.0306758\pi\)
−0.861821 + 0.507213i \(0.830676\pi\)
\(822\) 12.1920 37.5231i 0.425244 1.30877i
\(823\) −37.3268 27.1195i −1.30113 0.945326i −0.301164 0.953572i \(-0.597375\pi\)
−0.999966 + 0.00824607i \(0.997375\pi\)
\(824\) −0.465652 −0.0162217
\(825\) 0 0
\(826\) 17.5640 0.611131
\(827\) 37.7894 + 27.4556i 1.31407 + 0.954725i 0.999986 + 0.00532868i \(0.00169618\pi\)
0.314080 + 0.949396i \(0.398304\pi\)
\(828\) −2.06903 + 6.36782i −0.0719037 + 0.221297i
\(829\) 1.24396 + 3.82852i 0.0432046 + 0.132970i 0.970332 0.241776i \(-0.0777299\pi\)
−0.927127 + 0.374746i \(0.877730\pi\)
\(830\) 10.3718 7.53553i 0.360009 0.261562i
\(831\) −59.5146 + 43.2399i −2.06454 + 1.49997i
\(832\) 12.0517 + 37.0912i 0.417816 + 1.28591i
\(833\) −1.29523 + 3.98632i −0.0448772 + 0.138118i
\(834\) 21.7880 + 15.8299i 0.754458 + 0.548146i
\(835\) 87.3534 3.02299
\(836\) 0 0
\(837\) 2.56020 0.0884933
\(838\) −20.7517 15.0770i −0.716857 0.520827i
\(839\) −4.41960 + 13.6021i −0.152582 + 0.469598i −0.997908 0.0646525i \(-0.979406\pi\)
0.845326 + 0.534250i \(0.179406\pi\)
\(840\) −9.85533 30.3316i −0.340041 1.04654i
\(841\) 20.4310 14.8440i 0.704518 0.511863i
\(842\) −23.1590 + 16.8260i −0.798110 + 0.579861i
\(843\) 11.7002 + 36.0096i 0.402977 + 1.24024i
\(844\) −2.52758 + 7.77908i −0.0870028 + 0.267767i
\(845\) 20.7873 + 15.1028i 0.715104 + 0.519554i
\(846\) 48.5792 1.67019
\(847\) 0 0
\(848\) 12.4002 0.425823
\(849\) −46.9738 34.1285i −1.61214 1.17129i
\(850\) 19.4112 59.7417i 0.665800 2.04912i
\(851\) −1.10050 3.38698i −0.0377245 0.116104i
\(852\) −0.168519 + 0.122436i −0.00577335 + 0.00419459i
\(853\) −26.1318 + 18.9859i −0.894735 + 0.650063i −0.937108 0.349038i \(-0.886508\pi\)
0.0423729 + 0.999102i \(0.486508\pi\)
\(854\) 4.62612 + 14.2377i 0.158303 + 0.487205i
\(855\) −5.74075 + 17.6682i −0.196330 + 0.604240i
\(856\) 19.4526 + 14.1331i 0.664875 + 0.483060i
\(857\) −16.2318 −0.554468 −0.277234 0.960802i \(-0.589418\pi\)
−0.277234 + 0.960802i \(0.589418\pi\)
\(858\) 0 0
\(859\) −28.2893 −0.965220 −0.482610 0.875835i \(-0.660311\pi\)
−0.482610 + 0.875835i \(0.660311\pi\)
\(860\) 1.65952 + 1.20571i 0.0565890 + 0.0411143i
\(861\) −3.82597 + 11.7751i −0.130389 + 0.401295i
\(862\) 4.76754 + 14.6730i 0.162383 + 0.499764i
\(863\) −25.8776 + 18.8012i −0.880885 + 0.640001i −0.933486 0.358615i \(-0.883249\pi\)
0.0526003 + 0.998616i \(0.483249\pi\)
\(864\) −2.73872 + 1.98980i −0.0931731 + 0.0676942i
\(865\) 24.5764 + 75.6384i 0.835622 + 2.57178i
\(866\) 0.119312 0.367204i 0.00405438 0.0124781i
\(867\) 1.18447 + 0.860569i 0.0402268 + 0.0292265i
\(868\) −0.578830 −0.0196468
\(869\) 0 0
\(870\) −26.0403 −0.882848
\(871\) −26.9718 19.5962i −0.913905 0.663991i
\(872\) 4.59530 14.1429i 0.155617 0.478938i
\(873\) −12.2749 37.7782i −0.415442 1.27860i
\(874\) 6.41219 4.65873i 0.216896 0.157584i
\(875\) −22.3092 + 16.2086i −0.754189 + 0.547951i
\(876\) −3.23482 9.95574i −0.109294 0.336373i
\(877\) −14.1520 + 43.5553i −0.477878 + 1.47076i 0.364157 + 0.931337i \(0.381357\pi\)
−0.842036 + 0.539421i \(0.818643\pi\)
\(878\) 3.64144 + 2.64566i 0.122893 + 0.0892867i
\(879\) 43.3496 1.46215
\(880\) 0 0
\(881\) 26.7142 0.900025 0.450012 0.893022i \(-0.351420\pi\)
0.450012 + 0.893022i \(0.351420\pi\)
\(882\) 3.75507 + 2.72822i 0.126440 + 0.0918639i
\(883\) −8.80295 + 27.0927i −0.296243 + 0.911742i 0.686558 + 0.727075i \(0.259121\pi\)
−0.982801 + 0.184667i \(0.940879\pi\)
\(884\) 2.10647 + 6.48304i 0.0708481 + 0.218048i
\(885\) −117.319 + 85.2370i −3.94362 + 2.86521i
\(886\) −22.5600 + 16.3908i −0.757918 + 0.550660i
\(887\) 7.29711 + 22.4582i 0.245013 + 0.754072i 0.995634 + 0.0933398i \(0.0297543\pi\)
−0.750621 + 0.660733i \(0.770246\pi\)
\(888\) 1.72539 5.31021i 0.0579004 0.178199i
\(889\) 8.73362 + 6.34535i 0.292916 + 0.212816i
\(890\) 21.9604 0.736113
\(891\) 0 0
\(892\) 3.17572 0.106331
\(893\) 10.5740 + 7.68246i 0.353845 + 0.257084i
\(894\) −12.2773 + 37.7856i −0.410614 + 1.26374i
\(895\) −22.7533 70.0274i −0.760559 2.34076i
\(896\) −5.82947 + 4.23536i −0.194749 + 0.141493i
\(897\) 45.4964 33.0551i 1.51908 1.10368i
\(898\) −3.66934 11.2931i −0.122448 0.376855i
\(899\) −0.934665 + 2.87660i −0.0311728 + 0.0959401i
\(900\) 12.7906 + 9.29292i 0.426353 + 0.309764i
\(901\) 16.6477 0.554614
\(902\) 0 0
\(903\) −3.48696 −0.116039
\(904\) −7.44715 5.41067i −0.247689 0.179956i
\(905\) −19.1640 + 58.9809i −0.637034 + 1.96059i
\(906\) 7.06102 + 21.7316i 0.234587 + 0.721984i
\(907\) −19.3706 + 14.0736i −0.643192 + 0.467306i −0.860945 0.508698i \(-0.830127\pi\)
0.217754 + 0.976004i \(0.430127\pi\)
\(908\) 7.96189 5.78465i 0.264225 0.191970i
\(909\) −8.27599 25.4709i −0.274497 0.844816i
\(910\) −7.08688 + 21.8112i −0.234928 + 0.723034i
\(911\) −14.7555 10.7205i −0.488873 0.355187i 0.315878 0.948800i \(-0.397701\pi\)
−0.804751 + 0.593613i \(0.797701\pi\)
\(912\) 10.0435 0.332572
\(913\) 0 0
\(914\) −14.4463 −0.477841
\(915\) −99.9947 72.6504i −3.30572 2.40175i
\(916\) −1.30608 + 4.01971i −0.0431541 + 0.132815i
\(917\) −2.68977 8.27827i −0.0888241 0.273373i
\(918\) 7.09154 5.15231i 0.234056 0.170052i
\(919\) 22.9780 16.6945i 0.757975 0.550701i −0.140313 0.990107i \(-0.544811\pi\)
0.898289 + 0.439406i \(0.144811\pi\)
\(920\) −19.0210 58.5406i −0.627104 1.93003i
\(921\) 0.189739 0.583956i 0.00625211 0.0192420i
\(922\) 0.701061 + 0.509350i 0.0230882 + 0.0167746i
\(923\) 0.958607 0.0315529
\(924\) 0 0
\(925\) −8.40922 −0.276493
\(926\) −13.9357 10.1249i −0.457956 0.332725i
\(927\) −0.172902 + 0.532138i −0.00567885 + 0.0174777i
\(928\) −1.23587 3.80361i −0.0405694 0.124860i
\(929\) −2.74227 + 1.99237i −0.0899709 + 0.0653677i −0.631861 0.775081i \(-0.717709\pi\)
0.541890 + 0.840449i \(0.317709\pi\)
\(930\) −17.0109 + 12.3591i −0.557808 + 0.405271i
\(931\) 0.385900 + 1.18768i 0.0126474 + 0.0389246i
\(932\) 3.04599 9.37460i 0.0997748 0.307075i
\(933\) −1.36823 0.994078i −0.0447939 0.0325446i
\(934\) −37.8588 −1.23878
\(935\) 0 0
\(936\) 48.3096 1.57905
\(937\) 36.7190 + 26.6779i 1.19956 + 0.871529i 0.994241 0.107167i \(-0.0341780\pi\)
0.205315 + 0.978696i \(0.434178\pi\)
\(938\) 2.99518 9.21822i 0.0977962 0.300986i
\(939\) 5.93257 + 18.2586i 0.193602 + 0.595846i
\(940\) 12.8314 9.32258i 0.418515 0.304069i
\(941\) 17.4164 12.6538i 0.567759 0.412501i −0.266531 0.963826i \(-0.585878\pi\)
0.834291 + 0.551325i \(0.185878\pi\)
\(942\) 10.6630 + 32.8172i 0.347418 + 1.06924i
\(943\) −7.38420 + 22.7262i −0.240463 + 0.740068i
\(944\) 34.7519 + 25.2488i 1.13108 + 0.821777i
\(945\) −6.70272 −0.218039
\(946\) 0 0
\(947\) −11.2673 −0.366140 −0.183070 0.983100i \(-0.558603\pi\)
−0.183070 + 0.983100i \(0.558603\pi\)
\(948\) −3.52178 2.55872i −0.114382 0.0831035i
\(949\) −14.8867 + 45.8167i −0.483244 + 1.48727i
\(950\) −5.78336 17.7994i −0.187637 0.577487i
\(951\) 36.3484 26.4087i 1.17868 0.856359i
\(952\) −10.2609 + 7.45496i −0.332557 + 0.241617i
\(953\) 7.37612 + 22.7014i 0.238936 + 0.735370i 0.996575 + 0.0826956i \(0.0263529\pi\)
−0.757639 + 0.652674i \(0.773647\pi\)
\(954\) 5.69679 17.5329i 0.184440 0.567649i
\(955\) −78.6380 57.1339i −2.54467 1.84881i
\(956\) −2.78262 −0.0899964
\(957\) 0 0
\(958\) 6.00159 0.193902
\(959\) 9.70634 + 7.05207i 0.313434 + 0.227723i
\(960\) 28.9281 89.0316i 0.933651 2.87348i
\(961\) −8.82482 27.1600i −0.284672 0.876129i
\(962\) −3.24823 + 2.35998i −0.104727 + 0.0760888i
\(963\) 23.3740 16.9822i 0.753217 0.547244i
\(964\) 3.14051 + 9.66548i 0.101149 + 0.311304i
\(965\) 17.7741 54.7030i 0.572168 1.76095i
\(966\) 13.2271 + 9.61007i 0.425576 + 0.309199i
\(967\) −20.5165 −0.659765 −0.329882 0.944022i \(-0.607009\pi\)
−0.329882 + 0.944022i \(0.607009\pi\)
\(968\) 0 0
\(969\) 13.4837 0.433159
\(970\) 46.1629 + 33.5393i 1.48220 + 1.07688i
\(971\) −10.7428 + 33.0630i −0.344754 + 1.06104i 0.616962 + 0.786993i \(0.288363\pi\)
−0.961715 + 0.274050i \(0.911637\pi\)
\(972\) −2.53432 7.79982i −0.0812882 0.250179i
\(973\) −6.62558 + 4.81377i −0.212406 + 0.154322i
\(974\) 33.4344 24.2915i 1.07131 0.778350i
\(975\) −41.0347 126.292i −1.31416 4.04457i
\(976\) −11.3139 + 34.8207i −0.362150 + 1.11458i
\(977\) −4.67850 3.39913i −0.149678 0.108748i 0.510426 0.859922i \(-0.329488\pi\)
−0.660104 + 0.751174i \(0.729488\pi\)
\(978\) −25.7074 −0.822032
\(979\) 0 0
\(980\) 1.51540 0.0484078
\(981\) −14.4559 10.5028i −0.461542 0.335330i
\(982\) −2.70453 + 8.32369i −0.0863050 + 0.265620i
\(983\) −5.32500 16.3887i −0.169841 0.522718i 0.829519 0.558478i \(-0.188615\pi\)
−0.999360 + 0.0357606i \(0.988615\pi\)
\(984\) −30.3094 + 22.0211i −0.966229 + 0.702007i
\(985\) −59.8008 + 43.4478i −1.90541 + 1.38436i
\(986\) 3.20012 + 9.84895i 0.101912 + 0.313654i
\(987\) −8.33150 + 25.6417i −0.265195 + 0.816185i
\(988\) 1.64307 + 1.19376i 0.0522731 + 0.0379786i
\(989\) −6.72991 −0.213999
\(990\) 0 0
\(991\) −24.0077 −0.762630 −0.381315 0.924445i \(-0.624529\pi\)
−0.381315 + 0.924445i \(0.624529\pi\)
\(992\) −2.61259 1.89815i −0.0829497 0.0602665i
\(993\) 22.7783 70.1044i 0.722847 2.22469i
\(994\) 0.0861214 + 0.265054i 0.00273161 + 0.00840702i
\(995\) 5.10983 3.71251i 0.161993 0.117695i
\(996\) 1.89469 1.37657i 0.0600355 0.0436184i
\(997\) −11.1350 34.2699i −0.352648 1.08534i −0.957361 0.288895i \(-0.906712\pi\)
0.604713 0.796443i \(-0.293288\pi\)
\(998\) −4.32628 + 13.3149i −0.136946 + 0.421476i
\(999\) −0.949348 0.689741i −0.0300360 0.0218225i
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 847.2.f.z.323.4 24
11.2 odd 10 847.2.f.y.148.4 24
11.3 even 5 inner 847.2.f.z.729.4 24
11.4 even 5 inner 847.2.f.z.372.3 24
11.5 even 5 847.2.a.m.1.3 6
11.6 odd 10 847.2.a.n.1.4 yes 6
11.7 odd 10 847.2.f.y.372.4 24
11.8 odd 10 847.2.f.y.729.3 24
11.9 even 5 inner 847.2.f.z.148.3 24
11.10 odd 2 847.2.f.y.323.3 24
33.5 odd 10 7623.2.a.cs.1.4 6
33.17 even 10 7623.2.a.cp.1.3 6
77.6 even 10 5929.2.a.bm.1.4 6
77.27 odd 10 5929.2.a.bj.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.m.1.3 6 11.5 even 5
847.2.a.n.1.4 yes 6 11.6 odd 10
847.2.f.y.148.4 24 11.2 odd 10
847.2.f.y.323.3 24 11.10 odd 2
847.2.f.y.372.4 24 11.7 odd 10
847.2.f.y.729.3 24 11.8 odd 10
847.2.f.z.148.3 24 11.9 even 5 inner
847.2.f.z.323.4 24 1.1 even 1 trivial
847.2.f.z.372.3 24 11.4 even 5 inner
847.2.f.z.729.4 24 11.3 even 5 inner
5929.2.a.bj.1.3 6 77.27 odd 10
5929.2.a.bm.1.4 6 77.6 even 10
7623.2.a.cp.1.3 6 33.17 even 10
7623.2.a.cs.1.4 6 33.5 odd 10